B:=[];
G:=[];
# Design 1: autom. group order 6, simple, residual
B[1]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,8,10,11],[1,2,3,7,10,11,12],[1,2,3,9,12,13,14],[1,2,4,5,10,13,14],[1,3,6,9,12,13,14],[1,4,6,7,8,9,13],[1,4,6,7,10,12,14],[1,4,8,9,10,11,14],[1,5,6,8,11,12,13],[1,5,7,8,11,12,14],[1,5,7,9,10,11,13],[2,3,7,8,11,13,14],[2,4,6,8,11,13,14],[2,4,6,9,10,11,12],[2,4,7,9,11,12,13],[2,5,6,7,8,9,12],[2,5,6,7,10,13,14],[2,5,8,9,10,12,14],[3,4,5,6,11,12,14],[3,4,5,7,9,11,14],[3,4,5,8,10,12,13],[3,4,7,8,10,12,13],[3,5,6,9,10,11,13],[3,6,7,8,9,10,14]];
G[1]:=Group([(1,4)(2,5)(6,7)(8,9)(10,14),(1,8,14,4,9,10)(2,5)(3,12,13)(6,7)]);
# Design 2: autom. group order 6, simple, residual
B[2]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,7,10,11],[1,2,3,8,10,12,13],[1,2,3,9,12,13,14],[1,2,4,6,11,12,14],[1,3,5,7,11,13,14],[1,4,6,8,9,10,13],[1,4,6,8,11,12,14],[1,4,7,9,10,13,14],[1,5,6,8,9,11,13],[1,5,7,8,10,12,14],[1,5,7,9,10,11,12],[2,3,8,9,10,11,14],[2,4,5,7,8,12,13],[2,4,5,9,10,11,14],[2,4,5,10,11,12,13],[2,5,6,7,8,9,14],[2,6,7,8,10,11,13],[2,6,7,9,12,13,14],[3,4,5,6,10,13,14],[3,4,6,7,9,10,12],[3,4,7,8,9,11,12],[3,4,7,8,11,13,14],[3,5,6,8,10,12,14],[3,5,6,9,11,12,13]];
G[2]:=Group([(1,4,12)(3,5,13)(6,11,14)(7,10,9),(1,6)(3,7)(4,11)(5,10)(9,13)(12,14)]);
# Design 3: autom. group order 6, simple, residual
B[3]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,8,10,11],[1,2,3,7,12,13,14],[1,2,3,9,10,11,12],[1,2,4,6,10,13,14],[1,3,5,9,11,13,14],[1,4,6,7,11,12,13],[1,4,7,8,9,11,12],[1,4,8,9,10,13,14],[1,5,6,7,8,10,12],[1,5,6,8,11,13,14],[1,5,7,9,10,12,14],[2,3,7,8,12,13,14],[2,4,5,6,9,12,14],[2,4,5,7,10,11,13],[2,4,5,8,11,12,14],[2,5,7,9,10,11,13],[2,6,7,8,9,10,14],[2,6,8,9,11,12,13],[3,4,5,8,10,12,13],[3,4,6,7,9,11,14],[3,4,6,9,10,12,13],[3,4,7,8,10,11,14],[3,5,6,7,8,9,13],[3,5,6,10,11,12,14]];
G[3]:=Group([(2,7,13)(3,12,14)(5,11,10),(1,4)(3,5)(8,9)(10,14)(11,12)]);
# Design 4: autom. group order 6, simple, residual
B[4]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,7,10,11],[1,2,3,8,10,12,13],[1,2,3,9,12,13,14],[1,2,4,6,11,12,14],[1,3,5,7,11,13,14],[1,4,6,8,11,12,14],[1,4,7,8,9,11,13],[1,4,7,9,10,13,14],[1,5,6,8,9,10,12],[1,5,6,8,10,13,14],[1,5,7,9,10,11,12],[2,3,8,9,10,11,14],[2,4,5,7,8,12,13],[2,4,5,9,10,11,14],[2,4,5,10,11,12,13],[2,5,6,7,8,9,14],[2,6,7,8,10,11,13],[2,6,7,9,12,13,14],[3,4,5,6,10,13,14],[3,4,6,7,9,10,12],[3,4,6,8,9,11,13],[3,4,7,8,10,12,14],[3,5,6,9,11,12,13],[3,5,7,8,11,12,14]];
G[4]:=Group([(1,4,12)(3,5,13)(6,11,14)(7,10,9),(1,6)(3,7)(4,11)(5,10)(9,13)(12,14)]);
# Design 5: autom. group order 6, simple, residual
B[5]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,10,11,13,14],[1,4,6,8,12,13,14],[1,4,7,9,11,12,13],[1,5,6,9,10,12,14],[1,5,7,8,9,10,13],[1,6,7,8,10,11,12],[2,3,7,10,12,13,14],[2,4,5,8,9,12,13],[2,4,6,9,10,11,12],[2,4,7,8,9,10,14],[2,5,6,8,10,11,13],[2,5,7,8,11,12,14],[2,6,7,9,11,13,14],[3,4,5,7,10,11,13],[3,4,5,9,11,12,14],[3,4,6,7,8,12,13],[3,4,6,8,10,11,14],[3,5,6,7,9,10,12],[3,5,6,8,9,13,14]];
G[5]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,7)(3,14)]);
# Design 6: autom. group order 6, simple, residual
B[6]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,10,11,13,14],[1,4,6,8,12,13,14],[1,4,7,8,10,11,12],[1,5,6,9,10,12,14],[1,5,7,9,11,12,13],[1,6,7,8,9,10,13],[2,3,7,10,12,13,14],[2,4,5,9,10,11,13],[2,4,6,8,11,12,13],[2,4,7,9,11,12,14],[2,5,6,8,9,10,12],[2,5,7,8,9,13,14],[2,6,7,8,10,11,14],[3,4,5,7,8,10,13],[3,4,5,8,9,12,14],[3,4,6,7,9,12,13],[3,4,6,9,10,11,14],[3,5,6,7,10,11,12],[3,5,6,8,11,13,14]];
G[6]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,14)(3,7)(4,10,6,13,5,12)(8,11,9)]);
# Design 7: autom. group order 6, simple, residual
B[7]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,11,12,13,14],[1,4,6,8,10,12,14],[1,4,7,8,11,12,13],[1,5,6,9,10,13,14],[1,5,7,9,10,11,13],[1,6,7,8,9,10,12],[2,3,7,10,12,13,14],[2,4,5,9,10,11,12],[2,4,6,8,10,11,13],[2,4,7,9,10,11,14],[2,5,6,8,9,12,13],[2,5,7,8,9,12,14],[2,6,7,8,11,13,14],[3,4,5,7,8,10,13],[3,4,5,8,9,13,14],[3,4,6,7,9,12,13],[3,4,6,9,11,12,14],[3,5,6,7,10,11,12],[3,5,6,8,10,11,14]];
G[7]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,3)(4,10)(5,12)(6,13)(7,14)]);
# Design 8: autom. group order 6, simple
B[8]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,10,11,13,14],[1,4,6,8,12,13,14],[1,4,7,8,11,12,13],[1,5,6,9,10,12,14],[1,5,7,9,10,11,13],[1,6,7,8,9,10,12],[2,3,7,10,12,13,14],[2,4,5,9,10,11,12],[2,4,6,8,10,11,13],[2,4,7,8,9,10,14],[2,5,6,8,9,12,13],[2,5,7,8,11,12,14],[2,6,7,9,11,13,14],[3,4,5,7,9,12,13],[3,4,5,8,9,13,14],[3,4,6,7,10,11,12],[3,4,6,9,11,12,14],[3,5,6,7,8,10,13],[3,5,6,8,10,11,14]];
G[8]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,3)(4,10)(5,12)(6,13)(7,14)]);
# Design 9: autom. group order 6, simple, residual
B[9]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,11,12,13,14],[1,4,6,8,10,12,14],[1,4,7,8,10,11,13],[1,5,6,9,10,13,14],[1,5,7,9,10,11,12],[1,6,7,8,9,12,13],[2,3,7,10,12,13,14],[2,4,5,8,9,10,13],[2,4,6,9,11,12,13],[2,4,7,9,11,12,14],[2,5,6,8,10,11,12],[2,5,7,8,9,13,14],[2,6,7,8,10,11,14],[3,4,5,7,8,12,13],[3,4,5,9,10,11,14],[3,4,6,7,9,10,12],[3,4,6,8,11,13,14],[3,5,6,7,10,11,13],[3,5,6,8,9,12,14]];
G[9]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,3)(4,10)(5,13)(6,12)(7,14)(8,9)]);
# Design 10: autom. group order 6, simple, residual
B[10]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,10,11,13,14],[1,4,6,8,12,13,14],[1,4,7,8,9,10,12],[1,5,6,9,10,12,14],[1,5,7,8,11,12,13],[1,6,7,9,10,11,13],[2,3,7,10,12,13,14],[2,4,5,9,10,11,13],[2,4,6,8,11,12,13],[2,4,7,9,11,12,14],[2,5,6,8,9,10,12],[2,5,7,8,9,13,14],[2,6,7,8,10,11,14],[3,4,5,7,8,10,13],[3,4,5,9,11,12,14],[3,4,6,7,9,12,13],[3,4,6,8,10,11,14],[3,5,6,7,10,11,12],[3,5,6,8,9,13,14]];
G[10]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,14)(3,7)(4,10,6,13,5,12)(8,11,9)]);
# Design 11: autom. group order 6, simple, residual
B[11]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,11,12,13,14],[1,4,6,8,10,12,14],[1,4,7,8,9,12,13],[1,5,6,9,10,13,14],[1,5,7,8,10,11,13],[1,6,7,9,10,11,12],[2,3,7,10,12,13,14],[2,4,5,9,10,11,12],[2,4,6,8,10,11,13],[2,4,7,9,10,11,14],[2,5,6,8,9,12,13],[2,5,7,8,9,12,14],[2,6,7,8,11,13,14],[3,4,5,7,8,10,13],[3,4,5,9,11,13,14],[3,4,6,7,9,12,13],[3,4,6,8,11,12,14],[3,5,6,7,10,11,12],[3,5,6,8,9,10,14]];
G[11]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,3)(4,10)(5,12)(6,13)(7,14)]);
# Design 12: autom. group order 6, simple, residual
B[12]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,11,12,13,14],[1,4,6,8,10,12,14],[1,4,7,8,9,12,13],[1,5,6,9,10,13,14],[1,5,7,8,10,11,13],[1,6,7,9,10,11,12],[2,3,7,10,12,13,14],[2,4,5,9,10,11,13],[2,4,6,8,11,12,13],[2,4,7,8,10,11,14],[2,5,6,8,9,10,12],[2,5,7,9,11,12,14],[2,6,7,8,9,13,14],[3,4,5,7,9,10,12],[3,4,5,8,9,13,14],[3,4,6,7,10,11,13],[3,4,6,9,11,12,14],[3,5,6,7,8,12,13],[3,5,6,8,10,11,14]];
G[12]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,14)(3,7)(4,10)(5,13)(6,12)(9,11)]);
# Design 13: autom. group order 6, simple
B[13]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,10,11,13,14],[1,4,6,8,12,13,14],[1,4,7,8,9,10,12],[1,5,6,9,10,12,14],[1,5,7,8,11,12,13],[1,6,7,9,10,11,13],[2,3,7,10,12,13,14],[2,4,5,8,9,10,13],[2,4,6,9,11,12,13],[2,4,7,9,11,12,14],[2,5,6,8,10,11,12],[2,5,7,8,9,13,14],[2,6,7,8,10,11,14],[3,4,5,7,10,11,13],[3,4,5,9,11,12,14],[3,4,6,7,8,12,13],[3,4,6,8,10,11,14],[3,5,6,7,9,10,12],[3,5,6,8,9,13,14]];
G[13]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,14)(3,7)(4,10,6,13,5,12)(8,11,9)]);
# Design 14: autom. group order 6, simple, residual
B[14]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,10,11,13,14],[1,4,6,8,12,13,14],[1,4,7,8,9,12,13],[1,5,6,9,10,12,14],[1,5,7,8,10,11,13],[1,6,7,9,10,11,12],[2,3,7,10,12,13,14],[2,4,5,8,9,10,12],[2,4,6,9,10,11,13],[2,4,7,8,10,11,14],[2,5,6,8,11,12,13],[2,5,7,9,11,12,14],[2,6,7,8,9,13,14],[3,4,5,7,9,12,13],[3,4,5,9,11,13,14],[3,4,6,7,10,11,12],[3,4,6,8,11,12,14],[3,5,6,7,8,10,13],[3,5,6,8,9,10,14]];
G[14]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,3)(4,10)(5,12)(6,13)(7,14)]);
# Design 15: autom. group order 6, simple, residual
B[15]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,11,12,13,14],[1,4,6,8,10,12,14],[1,4,7,8,9,10,13],[1,5,6,9,10,13,14],[1,5,7,8,10,11,12],[1,6,7,9,11,12,13],[2,3,7,10,12,13,14],[2,4,5,8,9,12,13],[2,4,6,9,10,11,12],[2,4,7,8,11,13,14],[2,5,6,8,10,11,13],[2,5,7,9,10,11,14],[2,6,7,8,9,12,14],[3,4,5,7,9,12,13],[3,4,5,9,10,11,14],[3,4,6,7,10,11,12],[3,4,6,8,11,13,14],[3,5,6,7,8,10,13],[3,5,6,8,9,12,14]];
G[15]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,14)(3,7)(4,10,5,12,6,13)(8,9,11)]);
# Design 16: autom. group order 6, simple, residual
B[16]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,8,10,13,14],[1,4,6,9,12,13,14],[1,4,7,8,10,11,12],[1,5,6,10,11,12,14],[1,5,7,9,11,12,13],[1,6,7,8,9,10,13],[2,3,7,10,12,13,14],[2,4,5,9,10,11,13],[2,4,6,8,11,12,13],[2,4,7,9,11,12,14],[2,5,6,8,9,10,12],[2,5,7,8,9,13,14],[2,6,7,8,10,11,14],[3,4,5,7,10,11,13],[3,4,5,8,9,12,14],[3,4,6,7,8,12,13],[3,4,6,9,10,11,14],[3,5,6,7,9,10,12],[3,5,6,8,11,13,14]];
G[16]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,14)(3,7)(4,10,6,13,5,12)(8,11,9)]);
# Design 17: autom. group order 6, simple, residual
B[17]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,8,10,13,14],[1,4,6,9,12,13,14],[1,4,7,8,11,12,13],[1,5,6,10,11,12,14],[1,5,7,9,10,11,13],[1,6,7,8,9,10,12],[2,3,7,10,12,13,14],[2,4,5,9,10,11,12],[2,4,6,8,10,11,13],[2,4,7,9,10,11,14],[2,5,6,8,9,12,13],[2,5,7,8,9,12,14],[2,6,7,8,11,13,14],[3,4,5,7,11,12,13],[3,4,5,8,9,13,14],[3,4,6,7,8,10,12],[3,4,6,9,11,12,14],[3,5,6,7,9,10,13],[3,5,6,8,10,11,14]];
G[17]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,3)(4,10)(5,12)(6,13)(7,14)]);
# Design 18: autom. group order 6, simple, residual
B[18]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,8,12,13,14],[1,4,6,9,10,12,14],[1,4,7,8,10,11,13],[1,5,6,10,11,13,14],[1,5,7,9,10,11,12],[1,6,7,8,9,12,13],[2,3,7,10,12,13,14],[2,4,5,9,11,12,13],[2,4,6,8,10,11,12],[2,4,7,8,11,13,14],[2,5,6,8,9,10,13],[2,5,7,9,10,11,14],[2,6,7,8,9,12,14],[3,4,5,7,9,12,13],[3,4,5,8,9,10,14],[3,4,6,7,10,11,12],[3,4,6,9,11,13,14],[3,5,6,7,8,10,13],[3,5,6,8,11,12,14]];
G[18]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,14)(3,7)(4,10,5,12,6,13)(8,9,11)]);
# Design 19: autom. group order 6, simple, residual
B[19]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,8,12,13,14],[1,4,6,9,10,12,14],[1,4,7,8,11,12,13],[1,5,6,10,11,13,14],[1,5,7,9,10,11,13],[1,6,7,8,9,10,12],[2,3,7,10,12,13,14],[2,4,5,9,10,11,12],[2,4,6,8,10,11,13],[2,4,7,8,10,11,14],[2,5,6,8,9,12,13],[2,5,7,9,11,12,14],[2,6,7,8,9,13,14],[3,4,5,7,9,10,13],[3,4,5,8,9,13,14],[3,4,6,7,11,12,13],[3,4,6,9,11,12,14],[3,5,6,7,8,10,12],[3,5,6,8,10,11,14]];
G[19]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,3)(4,10)(5,12)(6,13)(7,14)]);
# Design 20: autom. group order 6, simple, residual
B[20]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,8,12,13,14],[1,4,6,9,10,12,14],[1,4,7,8,10,11,13],[1,5,6,10,11,13,14],[1,5,7,9,10,11,12],[1,6,7,8,9,12,13],[2,3,7,10,12,13,14],[2,4,5,8,9,10,13],[2,4,6,9,11,12,13],[2,4,7,9,11,12,14],[2,5,6,8,10,11,12],[2,5,7,8,9,13,14],[2,6,7,8,10,11,14],[3,4,5,7,11,12,13],[3,4,5,9,10,11,14],[3,4,6,7,8,10,12],[3,4,6,8,11,13,14],[3,5,6,7,9,10,13],[3,5,6,8,9,12,14]];
G[20]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,3)(4,10)(5,13)(6,12)(7,14)(8,9)]);
# Design 21: autom. group order 6, simple, residual
B[21]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,8,10,13,14],[1,4,6,9,12,13,14],[1,4,7,8,11,12,13],[1,5,6,10,11,12,14],[1,5,7,9,10,11,13],[1,6,7,8,9,10,12],[2,3,7,10,12,13,14],[2,4,5,8,9,12,13],[2,4,6,9,10,11,12],[2,4,7,8,10,11,14],[2,5,6,8,10,11,13],[2,5,7,9,11,12,14],[2,6,7,8,9,13,14],[3,4,5,7,9,10,12],[3,4,5,9,11,13,14],[3,4,6,7,10,11,13],[3,4,6,8,11,12,14],[3,5,6,7,8,12,13],[3,5,6,8,9,10,14]];
G[21]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,14)(3,7)(4,10)(5,13)(6,12)(9,11)]);
# Design 22: autom. group order 6, simple, residual
B[22]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,8,12,13,14],[1,4,6,9,10,12,14],[1,4,7,8,9,10,13],[1,5,6,10,11,13,14],[1,5,7,8,10,11,12],[1,6,7,9,11,12,13],[2,3,7,10,12,13,14],[2,4,5,9,11,12,13],[2,4,6,8,10,11,12],[2,4,7,8,11,13,14],[2,5,6,8,9,10,13],[2,5,7,9,10,11,14],[2,6,7,8,9,12,14],[3,4,5,7,9,12,13],[3,4,5,9,10,11,14],[3,4,6,7,10,11,12],[3,4,6,8,11,13,14],[3,5,6,7,8,10,13],[3,5,6,8,9,12,14]];
G[22]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,14)(3,7)(4,10,5,12,6,13)(8,9,11)]);
# Design 23: autom. group order 6, simple, residual
B[23]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,9,11,13],[1,2,3,10,12,13,14],[1,2,4,5,6,7,14],[1,3,7,8,9,11,14],[1,4,5,8,12,13,14],[1,4,6,9,10,12,14],[1,4,7,8,9,12,13],[1,5,6,10,11,13,14],[1,5,7,8,10,11,13],[1,6,7,9,10,11,12],[2,3,7,10,12,13,14],[2,4,5,9,10,11,12],[2,4,6,8,10,11,13],[2,4,7,8,10,11,14],[2,5,6,8,9,12,13],[2,5,7,9,11,12,14],[2,6,7,8,9,13,14],[3,4,5,7,9,10,13],[3,4,5,9,11,13,14],[3,4,6,7,11,12,13],[3,4,6,8,11,12,14],[3,5,6,7,8,10,12],[3,5,6,8,9,10,14]];
G[23]:=Group([(4,5,6)(8,11,9)(10,12,13),(1,3)(4,10)(5,12)(6,13)(7,14)]);
# Design 24: autom. group order 6, simple, residual
B[24]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,11,12,13],[1,2,3,6,8,11,14],[1,2,3,7,9,12,14],[1,2,4,5,10,13,14],[1,3,6,9,10,12,13],[1,4,5,7,8,9,12],[1,4,6,9,11,13,14],[1,4,7,9,10,11,13],[1,5,6,8,12,13,14],[1,5,7,8,10,11,12],[1,6,7,8,10,11,14],[2,3,7,8,10,11,13],[2,4,5,6,8,9,11],[2,4,6,8,10,12,13],[2,4,7,8,12,13,14],[2,5,6,9,10,11,12],[2,5,7,9,11,13,14],[2,6,7,9,10,12,14],[3,4,5,6,7,10,14],[3,4,5,10,11,12,14],[3,4,6,7,11,12,13],[3,4,8,9,11,12,14],[3,5,6,7,8,9,13],[3,5,8,9,10,13,14]];
G[24]:=Group([(2,3)(4,9)(5,12)(6,14),(1,2)(6,7)(8,9)(11,12)]);
# Design 25: autom. group order 6, simple, residual
B[25]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,5,10,13,14],[1,2,6,7,10,11,13],[1,2,6,8,12,13,14],[1,3,6,7,9,12,14],[1,3,6,8,9,11,13],[1,4,5,7,11,12,14],[1,4,6,9,10,11,14],[1,4,7,8,9,13,14],[1,5,7,8,9,10,12],[1,5,8,10,11,12,13],[2,3,7,9,11,12,13],[2,3,8,9,10,12,14],[2,4,5,6,9,12,13],[2,4,6,8,11,12,14],[2,4,7,8,9,10,11],[2,5,6,7,8,10,14],[2,5,7,9,11,13,14],[3,4,5,8,11,13,14],[3,4,6,7,8,10,13],[3,4,7,10,12,13,14],[3,5,6,7,8,11,12],[3,5,6,9,10,11,14],[4,5,6,9,10,12,13]];
G[25]:=Group([(1,3)(4,5)(6,9)(7,8)(11,14)(12,13),(1,7,14)(3,11,8)(4,9,12)(5,13,6)]);
# Design 26: autom. group order 6, simple, residual
B[26]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,5,10,13,14],[1,2,6,7,10,11,13],[1,2,6,8,11,12,14],[1,3,6,7,9,12,14],[1,3,6,8,9,11,13],[1,4,5,7,12,13,14],[1,4,6,8,9,10,13],[1,4,9,10,12,13,14],[1,5,7,8,9,11,12],[1,5,7,8,10,11,14],[2,3,7,9,11,13,14],[2,3,8,9,10,12,14],[2,4,5,6,9,11,14],[2,4,6,7,8,10,12],[2,4,7,9,11,12,13],[2,5,6,8,12,13,14],[2,5,7,8,9,10,13],[3,4,5,8,11,12,13],[3,4,6,7,8,13,14],[3,4,7,8,10,11,14],[3,5,6,7,9,10,12],[3,5,6,10,11,12,13],[4,5,6,9,10,11,14]];
G[26]:=Group([(1,3)(4,5)(6,9)(7,8)(11,14)(12,13),(1,7,12)(3,13,8)(4,11,6)(5,9,14)]);
# Design 27: autom. group order 6, simple, residual
B[27]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,5,10,13,14],[1,2,6,7,8,11,13],[1,2,6,7,9,12,14],[1,3,6,7,10,12,14],[1,3,8,9,10,11,13],[1,4,5,8,9,12,14],[1,4,6,8,10,11,14],[1,4,6,9,11,12,13],[1,5,7,8,10,12,13],[1,5,7,9,11,13,14],[2,3,6,8,9,12,13],[2,3,7,8,9,11,14],[2,4,5,11,12,13,14],[2,4,6,8,10,13,14],[2,4,7,9,10,13,14],[2,5,6,9,10,11,12],[2,5,7,8,10,11,12],[3,4,5,6,7,11,13],[3,4,7,8,11,12,14],[3,4,7,9,10,12,13],[3,5,6,8,12,13,14],[3,5,6,9,10,11,14],[4,5,6,7,8,9,10]];
G[27]:=Group([(4,5)(6,7)(11,13)(12,14),(1,11,13)(3,12,14)(4,5,10)(6,7,8)]);
# Design 28: autom. group order 6, simple, residual
B[28]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,6,7,13,14],[1,2,5,8,9,10,13],[1,2,5,8,11,12,14],[1,3,6,9,10,11,14],[1,3,8,9,12,13,14],[1,4,5,6,11,13,14],[1,4,7,8,10,11,13],[1,4,7,9,10,12,14],[1,5,6,7,10,12,13],[1,6,7,8,9,11,12],[2,3,6,7,8,10,12],[2,3,7,9,11,13,14],[2,4,6,8,10,11,14],[2,4,6,9,11,12,13],[2,4,7,8,12,13,14],[2,5,6,9,10,12,14],[2,5,7,9,10,11,13],[3,4,5,7,9,11,12],[3,4,5,10,12,13,14],[3,4,6,8,9,10,13],[3,5,6,8,11,12,13],[3,5,7,8,10,11,14],[4,5,6,7,8,9,14]];
G[28]:=Group([(1,3,7,13,9,5)(4,6,14,11,10,8)]);
# Design 29: autom. group order 6, simple, residual
B[29]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,6,7,13,14],[1,2,5,8,9,10,13],[1,2,5,8,11,12,14],[1,3,6,9,10,11,13],[1,3,8,10,12,13,14],[1,4,5,7,11,12,13],[1,4,6,8,9,13,14],[1,4,7,9,10,11,14],[1,5,6,7,10,12,14],[1,6,7,8,9,11,12],[2,3,6,7,8,10,11],[2,3,7,9,12,13,14],[2,4,6,8,10,12,14],[2,4,6,9,11,12,13],[2,4,7,8,11,13,14],[2,5,6,9,10,11,14],[2,5,7,9,10,12,13],[3,4,5,6,9,12,14],[3,4,5,10,11,13,14],[3,4,7,8,9,10,12],[3,5,6,8,11,12,13],[3,5,7,8,9,11,14],[4,5,6,7,8,10,13]];
G[29]:=Group([(1,3,7,13,9,5)(4,6,14,12,10,8)]);
# Design 30: autom. group order 6, simple, residual
B[30]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,6,8,10,13],[1,2,5,7,11,13,14],[1,2,5,9,11,13,14],[1,3,6,7,11,12,14],[1,3,8,9,11,12,14],[1,4,5,7,9,10,12],[1,4,6,9,10,13,14],[1,4,7,8,10,13,14],[1,5,6,8,10,11,12],[1,6,7,8,9,12,13],[2,3,6,7,8,9,14],[2,3,7,9,10,12,13],[2,4,6,7,11,12,13],[2,4,6,8,10,11,14],[2,4,8,9,11,12,13],[2,5,6,9,10,12,14],[2,5,7,8,10,12,14],[3,4,5,6,12,13,14],[3,4,5,8,12,13,14],[3,4,7,9,10,11,14],[3,5,6,9,10,11,13],[3,5,7,8,10,11,13],[4,5,6,7,8,9,11]];
G[30]:=Group([(6,8)(7,9),(1,2,11)(3,4,12)(5,13,14)]);
# Design 31: autom. group order 6, simple
B[31]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,10,11,13,14],[1,2,5,6,7,12,13],[1,2,5,8,10,13,14],[1,3,6,7,9,11,13],[1,3,6,8,12,13,14],[1,4,5,9,11,12,14],[1,4,6,8,10,11,12],[1,4,7,9,12,13,14],[1,5,7,8,9,10,14],[1,6,7,8,9,10,11],[2,3,6,8,9,12,14],[2,3,7,8,9,10,12],[2,4,6,7,8,11,14],[2,4,7,8,11,13,14],[2,4,7,9,10,12,13],[2,5,6,9,10,11,13],[2,5,6,9,11,12,14],[3,4,5,6,7,10,14],[3,4,5,8,9,11,13],[3,4,6,9,10,13,14],[3,5,7,8,11,12,13],[3,5,7,10,11,12,14],[4,5,6,8,10,12,13]];
G[31]:=Group([(1,3,9,10,5,12)(2,8,7,14,11,4)]);
# Design 32: autom. group order 6, simple
B[32]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,6,10,13,14],[1,2,5,6,7,11,13],[1,2,7,8,9,11,14],[1,3,5,8,9,12,13],[1,3,8,10,11,12,13],[1,4,5,7,10,12,14],[1,4,6,8,9,11,14],[1,4,6,8,10,13,14],[1,5,7,9,10,12,14],[1,6,7,9,11,12,13],[2,3,7,8,11,12,14],[2,3,7,9,10,13,14],[2,4,5,11,12,13,14],[2,4,6,9,10,11,12],[2,4,7,8,9,10,13],[2,5,6,8,9,10,12],[2,5,6,8,12,13,14],[3,4,5,9,11,13,14],[3,4,6,7,8,12,14],[3,4,6,7,9,12,13],[3,5,6,7,8,10,11],[3,5,6,9,10,11,14],[4,5,7,8,10,11,13]];
G[32]:=Group([(1,5,14)(2,13,6)(3,11,8)(7,12,10),(1,7,14,10,5,12)(2,3,6,8,13,11)]);
# Design 33: autom. group order 6, simple
B[33]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,6,10,13,14],[1,2,5,6,7,11,13],[1,2,7,8,9,12,13],[1,3,5,8,9,10,14],[1,3,7,8,11,12,14],[1,4,5,11,12,13,14],[1,4,6,9,10,11,12],[1,4,7,8,9,10,13],[1,5,6,8,12,13,14],[1,6,7,9,10,11,14],[2,3,7,9,11,13,14],[2,3,8,10,11,12,13],[2,4,5,7,10,12,14],[2,4,6,8,9,11,14],[2,4,6,8,10,13,14],[2,5,6,8,9,11,12],[2,5,7,9,10,12,14],[3,4,5,9,11,13,14],[3,4,6,7,8,12,14],[3,4,6,7,9,12,13],[3,5,6,7,8,10,11],[3,5,6,9,10,12,13],[4,5,7,8,10,11,13]];
G[33]:=Group([(1,3,6,8,13,11)(2,7,14,10,5,12)]);
# Design 34: autom. group order 6, simple
B[34]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,6,10,13,14],[1,2,5,6,11,12,13],[1,2,7,8,10,11,12],[1,3,5,8,9,11,14],[1,3,9,10,11,13,14],[1,4,5,7,12,13,14],[1,4,6,8,9,12,14],[1,4,7,8,11,13,14],[1,5,6,7,9,10,13],[1,6,7,8,9,10,12],[2,3,7,8,9,12,13],[2,3,7,9,12,13,14],[2,4,5,8,9,10,13],[2,4,6,8,10,13,14],[2,4,6,9,11,12,14],[2,5,6,7,9,11,14],[2,5,7,8,10,11,14],[3,4,5,7,10,12,14],[3,4,6,7,8,11,13],[3,4,6,7,9,10,11],[3,5,6,8,10,12,14],[3,5,6,8,11,12,13],[4,5,9,10,11,12,13]];
G[34]:=Group([(1,4,6,10,5,11)(2,3,7,9,13,12)]);
# Design 35: autom. group order 6, simple, residual
B[35]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,6,7,13,14],[1,2,5,8,10,11,13],[1,2,6,9,10,12,13],[1,3,5,8,11,12,14],[1,3,7,9,10,12,14],[1,4,5,9,11,13,14],[1,4,6,8,9,12,13],[1,4,7,8,9,10,14],[1,5,6,7,10,11,12],[1,6,7,8,11,13,14],[2,3,6,7,8,9,11],[2,3,8,10,12,13,14],[2,4,5,7,10,13,14],[2,4,6,8,11,12,14],[2,4,7,9,11,12,14],[2,5,6,8,9,10,14],[2,5,7,9,11,12,13],[3,4,5,6,12,13,14],[3,4,6,9,10,11,13],[3,4,7,8,10,11,13],[3,5,6,9,10,11,14],[3,5,7,8,9,12,13],[4,5,6,7,8,10,12]];
G[35]:=Group([(2,3)(6,7)(10,12)(13,14),(1,10,12)(2,3,11)(5,13,14)(6,9,7)]);
# Design 36: autom. group order 6, simple, residual
B[36]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,6,8,13,14],[1,2,5,7,10,11,13],[1,2,6,10,11,12,14],[1,3,5,9,10,12,13],[1,3,7,8,12,13,14],[1,4,6,7,9,12,14],[1,4,6,8,9,10,11],[1,4,8,9,10,13,14],[1,5,6,7,8,11,13],[1,5,7,9,11,12,14],[2,3,6,7,9,10,14],[2,3,7,8,9,11,12],[2,4,5,6,12,13,14],[2,4,5,9,11,13,14],[2,4,7,8,10,12,13],[2,5,7,8,9,10,14],[2,6,8,9,11,12,13],[3,4,5,8,11,12,14],[3,4,6,7,9,11,13],[3,4,7,10,11,13,14],[3,5,6,8,10,11,14],[3,5,6,9,10,12,13],[4,5,6,7,8,10,12]];
G[36]:=Group([(2,4,8,14,7,11)(3,9,13,12,5,10)]);
# Design 37: autom. group order 6, simple, residual
B[37]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,6,8,13,14],[1,2,5,7,10,11,13],[1,2,6,9,10,13,14],[1,3,5,9,11,12,13],[1,3,8,10,11,12,14],[1,4,6,7,8,11,12],[1,4,6,7,11,13,14],[1,4,7,8,9,10,14],[1,5,6,8,9,12,13],[1,5,7,9,10,12,14],[2,3,6,7,9,10,12],[2,3,7,8,12,13,14],[2,4,5,6,10,12,14],[2,4,5,8,9,11,14],[2,4,9,11,12,13,14],[2,5,7,8,10,11,13],[2,6,7,8,9,11,12],[3,4,5,7,12,13,14],[3,4,6,9,10,11,13],[3,4,7,8,9,10,13],[3,5,6,7,9,11,14],[3,5,6,8,10,11,14],[4,5,6,8,10,12,13]];
G[37]:=Group([(2,5,13)(3,9,6)(4,12,14)(7,11,10),(2,7,13,10,5,11)(3,4,6,14,9,12)]);
# Design 38: autom. group order 6, simple, residual
B[38]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,6,10,13,14],[1,2,5,8,9,11,13],[1,2,6,8,10,13,14],[1,3,5,7,12,13,14],[1,3,7,8,9,11,14],[1,4,6,7,9,12,13],[1,4,6,9,11,12,13],[1,4,7,8,9,10,14],[1,5,6,8,10,11,12],[1,5,7,10,11,12,14],[2,3,6,7,8,11,12],[2,3,9,11,12,13,14],[2,4,5,6,7,11,14],[2,4,5,9,10,12,14],[2,4,7,8,10,12,13],[2,5,7,9,10,11,13],[2,6,7,8,9,12,14],[3,4,5,8,12,13,14],[3,4,6,9,10,11,14],[3,4,7,8,10,11,13],[3,5,6,7,9,10,13],[3,5,6,8,9,10,12],[4,5,6,8,11,13,14]];
G[38]:=Group([(2,12)(3,11)(4,10)(7,8)(9,14),(1,6,13)(2,4,14,12,10,9)(3,11)(7,8)]);
# Design 39: autom. group order 6, simple, residual
B[39]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,6,10,11,13],[1,2,5,7,12,13,14],[1,2,6,8,10,12,14],[1,3,5,8,9,12,13],[1,3,7,8,9,10,14],[1,4,6,8,11,12,14],[1,4,7,8,11,13,14],[1,4,7,9,10,11,13],[1,5,6,7,9,11,12],[1,5,6,9,10,13,14],[2,3,6,9,11,13,14],[2,3,7,8,9,11,14],[2,4,5,8,10,13,14],[2,4,5,9,11,12,14],[2,4,7,9,10,12,13],[2,5,6,7,8,11,13],[2,6,7,8,9,10,12],[3,4,5,6,7,10,14],[3,4,6,7,8,12,13],[3,4,6,9,12,13,14],[3,5,7,10,11,12,14],[3,5,8,10,11,12,13],[4,5,6,8,9,10,11]];
G[39]:=Group([(1,4,7,10,12,8)(2,6,14,11,13,9)]);
# Design 40: autom. group order 6, simple, residual
B[40]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,6,10,13,14],[1,2,5,7,8,10,13],[1,2,7,8,9,11,14],[1,3,6,8,11,12,14],[1,3,7,9,11,12,13],[1,4,5,6,9,12,14],[1,4,6,7,9,10,11],[1,4,8,10,11,13,14],[1,5,6,7,12,13,14],[1,5,8,9,10,12,13],[2,3,6,9,10,13,14],[2,3,7,8,9,12,14],[2,4,5,9,11,13,14],[2,4,6,7,8,12,13],[2,4,6,8,11,12,13],[2,5,6,9,10,11,12],[2,5,7,10,11,12,14],[3,4,5,7,11,13,14],[3,4,5,8,10,12,14],[3,4,7,9,10,12,13],[3,5,6,7,8,10,11],[3,5,6,8,9,11,13],[4,6,7,8,9,10,14]];
G[40]:=Group([(2,6,13)(3,14,10)(4,12,8),(1,11)(3,12)(4,10)(7,9)(8,14)]);
# Design 41: autom. group order 6, simple, residual
B[41]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,10,11,13,14],[1,2,5,6,8,10,12],[1,2,7,9,10,13,14],[1,3,6,7,9,12,13],[1,3,6,8,9,11,14],[1,4,5,6,7,13,14],[1,4,6,9,11,12,13],[1,4,7,8,10,12,14],[1,5,7,8,10,11,13],[1,5,8,9,11,12,14],[2,3,6,7,8,11,14],[2,3,7,8,9,12,13],[2,4,5,8,9,13,14],[2,4,6,9,10,12,14],[2,4,7,8,11,12,13],[2,5,6,7,11,12,14],[2,5,6,9,10,11,13],[3,4,5,7,9,10,11],[3,4,5,11,12,13,14],[3,4,6,8,10,13,14],[3,5,6,8,10,12,13],[3,5,7,9,10,12,14],[4,6,7,8,9,10,11]];
G[41]:=Group([(1,2)(6,8)(7,9),(1,6,7,2,8,9)(4,14,12)(5,11,13)]);
# Design 42: autom. group order 6, simple, residual
B[42]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,10,11,13,14],[1,2,5,6,8,10,12],[1,2,7,9,10,13,14],[1,3,6,7,9,12,13],[1,3,6,8,9,11,14],[1,4,5,6,9,13,14],[1,4,7,8,10,12,14],[1,4,8,9,11,12,13],[1,5,6,7,11,12,14],[1,5,7,8,10,11,13],[2,3,6,7,8,11,14],[2,3,7,8,9,12,13],[2,4,5,7,8,13,14],[2,4,6,7,11,12,13],[2,4,6,9,10,12,14],[2,5,6,9,10,11,13],[2,5,8,9,11,12,14],[3,4,5,7,9,10,11],[3,4,5,11,12,13,14],[3,4,6,8,10,13,14],[3,5,6,8,10,12,13],[3,5,7,9,10,12,14],[4,6,7,8,9,10,11]];
G[42]:=Group([(1,2)(6,8)(7,9),(1,6,7,2,8,9)(4,14,12)(5,11,13)]);
# Design 43: autom. group order 6, simple, residual
B[43]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,4,10,11,12],[1,2,3,10,11,13,14],[1,2,5,6,8,10,12],[1,2,7,9,10,13,14],[1,3,6,7,9,12,13],[1,3,6,8,9,11,14],[1,4,5,8,9,13,14],[1,4,6,7,11,12,13],[1,4,7,8,10,12,14],[1,5,6,9,11,12,14],[1,5,7,8,10,11,13],[2,3,6,7,8,11,14],[2,3,7,8,9,12,13],[2,4,5,6,7,13,14],[2,4,6,9,10,12,14],[2,4,8,9,11,12,13],[2,5,6,9,10,11,13],[2,5,7,8,11,12,14],[3,4,5,7,9,10,11],[3,4,5,11,12,13,14],[3,4,6,8,10,13,14],[3,5,6,8,10,12,13],[3,5,7,9,10,12,14],[4,6,7,8,9,10,11]];
G[43]:=Group([(1,2)(6,8)(7,9),(1,6,7,2,8,9)(4,14,12)(5,11,13)]);
# Design 44: autom. group order 6, simple
B[44]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,4,11,12,13],[1,2,3,5,8,9,14],[1,2,5,6,7,10,11],[1,2,5,8,12,13,14],[1,3,6,7,8,11,14],[1,3,6,10,11,12,14],[1,4,5,7,12,13,14],[1,4,5,9,10,11,13],[1,4,6,9,10,12,14],[1,6,7,8,9,12,13],[1,7,8,9,10,11,13],[2,3,6,9,11,12,13],[2,3,7,9,10,13,14],[2,4,6,7,8,9,12],[2,4,6,7,10,13,14],[2,4,8,10,11,12,14],[2,5,6,9,11,13,14],[2,5,7,8,10,11,12],[3,4,5,6,8,10,13],[3,4,5,7,9,11,12],[3,4,7,8,11,13,14],[3,5,6,8,10,12,13],[3,5,7,9,10,12,14],[4,5,6,8,9,11,14]];
G[44]:=Group([(1,2,7,14,11,9)(3,6,13,8,5,10)]);
# Design 45: autom. group order 6, simple
B[45]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,4,11,12,13],[1,2,3,5,8,11,14],[1,2,5,6,7,9,12],[1,2,5,8,10,13,14],[1,3,6,7,10,11,13],[1,3,6,9,10,12,14],[1,4,5,6,10,12,14],[1,4,7,8,9,13,14],[1,4,9,11,12,13,14],[1,5,7,8,9,11,12],[1,6,7,8,10,11,13],[2,3,6,8,12,13,14],[2,3,7,9,10,12,13],[2,4,5,6,9,11,13],[2,4,6,8,9,10,11],[2,4,7,10,11,12,14],[2,5,7,9,10,13,14],[2,6,7,8,11,12,14],[3,4,5,7,8,12,13],[3,4,5,7,10,11,14],[3,4,6,7,8,9,14],[3,5,6,9,11,13,14],[3,5,8,9,10,11,12],[4,5,6,8,10,12,13]];
G[45]:=Group([(1,6)(2,14)(4,9)(5,12)(7,10)(11,13),(1,7,11,6,10,13)(2,4,5,14,9,12)]);
# Design 46: autom. group order 6, simple, residual
B[46]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,4,11,12,13],[1,2,3,5,6,8,11],[1,2,5,6,9,12,14],[1,2,7,8,10,11,14],[1,3,5,10,12,13,14],[1,3,7,8,12,13,14],[1,4,5,9,10,11,13],[1,4,6,7,9,10,12],[1,4,6,7,11,13,14],[1,5,7,8,9,10,13],[1,6,8,9,11,12,14],[2,3,6,9,10,13,14],[2,3,7,9,10,11,14],[2,4,5,7,8,13,14],[2,4,5,7,9,12,14],[2,4,6,8,10,12,13],[2,5,8,9,11,12,13],[2,6,7,10,11,12,13],[3,4,5,10,11,12,14],[3,4,6,8,9,13,14],[3,4,7,8,9,11,12],[3,5,6,7,8,10,12],[3,5,6,7,9,11,13],[4,5,6,8,10,11,14]];
G[46]:=Group([(2,10)(3,9)(6,13)(7,11),(1,6)(2,5)(4,7)(9,12)]);
# Design 47: autom. group order 6, simple
B[47]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,4,11,12,13],[1,2,3,5,6,8,14],[1,2,5,9,11,12,14],[1,2,6,9,10,13,14],[1,3,5,7,10,11,14],[1,3,7,8,12,13,14],[1,4,5,8,10,12,13],[1,4,6,7,8,9,11],[1,4,6,10,11,13,14],[1,5,7,9,10,12,13],[1,6,7,8,9,11,12],[2,3,6,9,11,12,13],[2,3,7,8,9,10,13],[2,4,5,7,8,11,13],[2,4,5,7,9,12,14],[2,4,8,10,11,12,14],[2,5,6,7,10,11,13],[2,6,7,8,10,12,14],[3,4,5,6,9,10,12],[3,4,6,7,12,13,14],[3,4,7,9,10,11,14],[3,5,6,8,10,11,12],[3,5,8,9,11,13,14],[4,5,6,8,9,13,14]];
G[47]:=Group([(1,6)(2,14)(3,13)(5,10)(7,11)(8,9),(1,7,8,6,11,9)(2,5,13,14,10,3)]);
# Design 48: autom. group order 6, simple
B[48]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,4,11,12,13],[1,2,3,5,8,11,14],[1,2,5,9,10,12,14],[1,2,6,7,9,10,13],[1,3,5,6,8,13,14],[1,3,6,9,11,12,13],[1,4,5,7,10,12,14],[1,4,6,8,10,11,12],[1,4,7,8,9,13,14],[1,5,7,8,9,11,12],[1,6,7,10,11,13,14],[2,3,6,7,9,12,14],[2,3,7,8,10,12,13],[2,4,5,6,12,13,14],[2,4,5,9,10,11,13],[2,4,7,8,11,13,14],[2,5,6,7,8,9,11],[2,6,8,10,11,12,14],[3,4,5,6,7,10,11],[3,4,6,8,9,10,14],[3,4,7,9,11,12,14],[3,5,7,8,10,12,13],[3,5,9,10,11,13,14],[4,5,6,8,9,12,13]];
G[48]:=Group([(1,4,11,14,6,9)(3,13,8,12,7,10)]);
# Design 49: autom. group order 6, simple, residual
B[49]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,7,10,11],[1,2,3,10,11,12,13],[1,2,4,6,8,12,14],[1,2,4,9,10,12,14],[1,3,5,7,9,13,14],[1,3,5,8,11,13,14],[1,4,5,10,11,12,13],[1,4,6,8,11,13,14],[1,5,7,9,10,12,14],[1,6,7,8,9,10,11],[1,6,7,8,9,12,13],[2,3,6,7,12,13,14],[2,3,8,9,10,11,14],[2,4,5,7,8,10,13],[2,4,7,9,11,13,14],[2,5,6,8,9,10,13],[2,5,6,9,11,12,13],[2,5,7,8,11,12,14],[3,4,5,6,9,11,12],[3,4,6,9,10,13,14],[3,4,7,8,9,11,12],[3,4,7,8,10,12,13],[3,5,6,8,10,12,14],[4,5,6,7,10,11,14]];
G[49]:=Group([(2,3)(4,5)(6,7)(8,9)(10,11)(12,13),(2,6,11,3,7,10)(4,8,13,5,9,12)]);
# Design 50: autom. group order 6, simple, residual
B[50]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,7,10,11],[1,2,3,8,9,12,13],[1,2,4,6,10,12,14],[1,2,4,8,11,12,14],[1,3,5,7,11,13,14],[1,3,5,9,10,13,14],[1,4,5,10,11,12,13],[1,4,6,9,10,13,14],[1,5,7,8,11,12,14],[1,6,7,8,9,10,11],[1,6,7,8,9,12,13],[2,3,6,7,12,13,14],[2,3,8,9,10,11,14],[2,4,5,7,8,10,13],[2,4,7,9,11,13,14],[2,5,6,8,10,11,13],[2,5,6,9,11,12,13],[2,5,7,9,10,12,14],[3,4,5,6,9,11,12],[3,4,6,8,11,13,14],[3,4,7,8,10,12,13],[3,4,7,9,10,11,12],[3,5,6,8,10,12,14],[4,5,6,7,8,9,14]];
G[50]:=Group([(2,3)(4,5)(6,7)(8,9)(10,11)(12,13),(2,6,9,3,7,8)(4,10,13,5,11,12)]);
# Design 51: autom. group order 6, simple
B[51]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,6,8],[1,2,3,7,9,10,11],[1,2,3,8,9,10,12],[1,2,4,9,11,13,14],[1,2,4,9,12,13,14],[1,3,5,7,12,13,14],[1,3,5,10,11,12,13],[1,4,6,7,10,11,13],[1,4,6,8,10,12,13],[1,5,6,8,9,11,14],[1,5,7,8,11,12,14],[1,6,7,8,9,10,14],[2,3,6,8,11,13,14],[2,3,7,8,10,13,14],[2,4,5,7,10,11,14],[2,4,5,8,10,12,14],[2,5,6,7,9,12,13],[2,5,6,9,10,11,12],[2,6,7,8,11,12,13],[3,4,5,8,9,11,13],[3,4,6,7,9,12,14],[3,4,6,10,11,12,14],[3,4,7,8,9,11,12],[3,5,6,9,10,13,14],[4,5,7,8,9,10,13]];
G[51]:=Group([(3,9)(5,14)(6,13)(7,11)(8,12),(1,2,4)(3,5,6)(9,14,13)]);
# Design 52: autom. group order 6, simple, residual
B[52]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,7,10,11],[1,2,3,8,9,10,12],[1,2,4,6,12,13,14],[1,2,4,8,11,13,14],[1,3,5,7,11,13,14],[1,3,5,9,12,13,14],[1,4,6,7,10,12,13],[1,4,8,9,10,11,13],[1,5,6,9,10,12,14],[1,5,7,8,10,11,14],[1,6,7,8,9,11,12],[2,3,6,8,11,12,14],[2,3,7,9,10,13,14],[2,4,5,7,9,11,12],[2,4,5,10,11,12,14],[2,5,6,9,10,11,13],[2,5,7,8,10,12,13],[2,6,7,8,9,13,14],[3,4,5,6,8,10,13],[3,4,6,9,10,11,14],[3,4,7,8,10,12,14],[3,4,7,9,11,12,13],[3,5,6,8,11,12,13],[4,5,6,7,8,9,14]];
G[52]:=Group([(6,8)(7,9)(11,12),(2,5,13)(3,14,4)(6,7,11,8,9,12)]);
# Design 53: autom. group order 6, simple, residual
B[53]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,7,10,11],[1,2,3,8,9,10,12],[1,2,4,6,11,13,14],[1,2,4,8,12,13,14],[1,3,5,7,12,13,14],[1,3,5,9,11,13,14],[1,4,6,9,10,11,13],[1,4,7,8,10,12,13],[1,5,6,7,10,12,14],[1,5,8,9,10,11,14],[1,6,7,8,9,11,12],[2,3,6,8,11,12,14],[2,3,7,9,10,13,14],[2,4,5,7,9,11,12],[2,4,5,10,11,12,14],[2,5,6,9,10,12,13],[2,5,7,8,10,11,13],[2,6,7,8,9,13,14],[3,4,5,6,8,10,13],[3,4,6,9,10,12,14],[3,4,7,8,10,11,14],[3,4,7,9,11,12,13],[3,5,6,8,11,12,13],[4,5,6,7,8,9,14]];
G[53]:=Group([(6,8)(7,9)(11,12),(2,5,13)(3,14,4)(6,7,12,8,9,11)]);
# Design 54: autom. group order 6, simple, residual
B[54]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,8,10,11],[1,2,3,7,9,10,12],[1,2,4,6,11,13,14],[1,2,4,9,12,13,14],[1,3,5,7,12,13,14],[1,3,5,8,11,13,14],[1,4,6,7,10,12,13],[1,4,8,9,10,11,13],[1,5,6,7,10,11,14],[1,5,8,9,10,12,14],[1,6,7,8,9,11,12],[2,3,6,9,11,12,14],[2,3,7,8,10,13,14],[2,4,5,7,8,11,12],[2,4,5,10,11,12,14],[2,5,6,8,10,12,13],[2,5,7,9,10,11,13],[2,6,7,8,9,13,14],[3,4,5,6,9,10,13],[3,4,6,8,10,12,14],[3,4,7,8,11,12,13],[3,4,7,9,10,11,14],[3,5,6,9,11,12,13],[4,5,6,7,8,9,14]];
G[54]:=Group([(6,9)(7,8)(11,12),(2,5,13)(3,14,4)(6,7,12,9,8,11)]);
# Design 55: autom. group order 6, simple, residual
B[55]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,10,11,12],[1,2,3,10,11,12,13],[1,2,4,6,8,13,14],[1,2,4,9,10,13,14],[1,3,5,7,9,11,14],[1,3,5,8,12,13,14],[1,4,6,7,11,12,14],[1,4,7,8,9,11,12],[1,5,6,7,9,10,13],[1,5,7,8,10,11,13],[1,6,8,9,10,12,14],[2,3,6,7,8,9,12],[2,3,7,8,11,13,14],[2,4,5,7,10,12,14],[2,4,5,9,11,12,13],[2,5,6,8,9,10,11],[2,5,7,8,10,12,14],[2,6,7,9,11,13,14],[3,4,5,6,10,11,14],[3,4,6,7,8,10,13],[3,4,7,9,10,12,13],[3,4,8,9,10,11,14],[3,5,6,9,12,13,14],[4,5,6,8,11,12,13]];
G[55]:=Group([(1,3,11)(2,10,12)(5,14,7),(1,5,3,14,11,7)(2,12,10)(4,13)(6,8)]);
# Design 56: autom. group order 6, simple
B[56]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,7,10,11],[1,2,3,10,11,12,13],[1,2,4,8,9,12,14],[1,2,4,10,12,13,14],[1,3,5,6,12,13,14],[1,3,5,8,9,11,13],[1,4,6,7,8,11,12],[1,4,6,9,10,11,14],[1,5,7,8,10,13,14],[1,5,7,9,10,11,14],[1,6,7,8,9,12,13],[2,3,6,8,9,10,14],[2,3,7,8,11,12,14],[2,4,5,6,7,13,14],[2,4,5,8,10,11,13],[2,5,6,9,11,12,13],[2,5,7,9,11,12,14],[2,6,7,8,9,10,13],[3,4,5,7,9,10,12],[3,4,6,9,11,13,14],[3,4,7,8,11,13,14],[3,4,7,9,10,12,13],[3,5,6,8,10,12,14],[4,5,6,8,10,11,12]];
G[56]:=Group([(1,2)(3,4)(6,8)(7,9)(10,12)(11,14),(1,6,11)(2,8,14)(3,12,9)(4,10,7)]);
# Design 57: autom. group order 6, simple
B[57]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,8,10,11],[1,2,3,10,12,13,14],[1,2,4,7,9,12,13],[1,2,4,10,11,12,14],[1,3,5,6,12,13,14],[1,3,5,7,9,11,14],[1,4,6,7,10,11,13],[1,4,6,8,9,11,12],[1,5,7,8,11,12,13],[1,5,8,9,10,13,14],[1,6,7,8,9,10,14],[2,3,6,7,9,10,13],[2,3,8,9,11,12,13],[2,4,5,6,8,13,14],[2,4,5,9,10,11,14],[2,5,6,7,11,12,14],[2,5,7,8,10,11,13],[2,6,7,8,9,12,14],[3,4,5,7,8,10,12],[3,4,6,8,11,13,14],[3,4,7,8,10,12,14],[3,4,7,9,11,13,14],[3,5,6,9,10,11,12],[4,5,6,9,10,12,13]];
G[57]:=Group([(1,2)(3,4)(6,9)(7,8)(10,12)(11,13),(1,6,11)(2,9,13)(3,12,7)(4,10,8)]);
# Design 58: autom. group order 6, simple, residual
B[58]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,6,8],[1,2,3,7,9,10,11],[1,2,3,9,10,11,12],[1,2,4,7,12,13,14],[1,2,4,9,12,13,14],[1,3,5,7,10,13,14],[1,3,6,8,11,13,14],[1,4,5,8,9,10,13],[1,4,6,8,9,11,12],[1,5,6,10,11,12,14],[1,5,7,8,11,12,13],[1,6,7,8,9,10,14],[2,3,5,8,9,12,14],[2,3,6,8,10,12,13],[2,4,5,8,10,11,14],[2,4,7,8,10,11,14],[2,5,6,7,9,11,13],[2,5,6,9,11,13,14],[2,6,7,8,10,12,13],[3,4,5,10,11,12,13],[3,4,6,7,11,12,14],[3,4,6,9,10,13,14],[3,4,7,8,9,11,13],[3,5,7,8,9,12,14],[4,5,6,7,9,10,12]];
G[58]:=Group([(1,4)(3,14)(5,12)(6,13)(8,9)(10,11),(1,6,11)(3,5,9)(4,13,10)(8,14,12)]);
# Design 59: autom. group order 6, simple, residual
B[59]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,10,11,12],[1,2,3,8,9,10,13],[1,2,4,6,7,13,14],[1,2,4,8,10,11,14],[1,3,5,6,12,13,14],[1,3,7,8,11,13,14],[1,4,5,9,11,12,13],[1,4,6,9,10,12,14],[1,5,7,8,10,12,13],[1,5,7,9,10,11,14],[1,6,7,8,9,11,12],[2,3,5,9,11,12,14],[2,3,7,9,10,12,13],[2,4,5,7,8,11,12],[2,4,7,9,12,13,14],[2,5,6,7,10,11,13],[2,5,6,8,10,12,14],[2,6,8,9,11,13,14],[3,4,5,10,11,13,14],[3,4,6,7,9,10,11],[3,4,6,8,11,12,13],[3,4,7,8,10,12,14],[3,5,6,7,8,9,14],[4,5,6,8,9,10,13]];
G[59]:=Group([(1,3,9,13,7,4)(5,8,10,12,14,6)]);
# Design 60: autom. group order 6, simple
B[60]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,10,11,12],[1,2,3,8,10,13,14],[1,2,4,6,9,10,13],[1,2,4,8,11,12,14],[1,3,5,7,10,13,14],[1,3,6,7,11,12,13],[1,4,5,9,11,12,13],[1,4,6,7,8,11,14],[1,5,6,9,10,12,14],[1,5,7,8,9,11,13],[1,7,8,9,10,12,14],[2,3,5,9,11,12,14],[2,3,7,9,11,13,14],[2,4,5,7,10,11,14],[2,4,7,9,10,12,13],[2,5,6,7,8,12,13],[2,5,6,8,12,13,14],[2,6,7,8,9,10,11],[3,4,5,7,8,10,12],[3,4,6,7,9,12,14],[3,4,6,8,9,13,14],[3,4,8,10,11,12,13],[3,5,6,8,9,10,11],[4,5,6,10,11,13,14]];
G[60]:=Group([(1,3,4,10,9,11)(2,8,13,6,5,12)]);
# Design 61: autom. group order 6, simple, residual
B[61]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,10,11,12],[1,2,3,8,10,13,14],[1,2,4,7,10,11,13],[1,2,4,9,12,13,14],[1,3,5,6,7,13,14],[1,3,6,8,9,12,14],[1,4,5,8,9,10,11],[1,4,6,7,9,11,12],[1,5,7,11,12,13,14],[1,5,8,10,11,12,14],[1,6,7,8,9,10,13],[2,3,5,7,8,11,12],[2,3,7,9,10,11,14],[2,4,5,6,10,12,14],[2,4,6,8,11,13,14],[2,5,6,9,10,12,13],[2,5,7,8,9,12,13],[2,6,7,8,9,11,14],[3,4,5,9,11,13,14],[3,4,6,8,11,12,13],[3,4,7,8,10,12,13],[3,4,7,9,10,12,14],[3,5,6,9,10,11,13],[4,5,6,7,8,10,14]];
G[61]:=Group([(2,6,13,12,10,9)(3,7,14,11,8,4)]);
# Design 62: autom. group order 6, simple, residual
B[62]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,10,11,12],[1,2,3,8,10,11,13],[1,2,4,7,10,13,14],[1,2,4,9,12,13,14],[1,3,5,6,7,12,14],[1,3,6,8,9,11,14],[1,4,5,10,11,12,14],[1,4,6,7,8,11,13],[1,5,7,8,9,10,12],[1,5,7,9,10,11,13],[1,6,8,9,12,13,14],[2,3,5,11,12,13,14],[2,3,7,8,9,10,14],[2,4,5,8,9,11,12],[2,4,6,7,9,11,14],[2,5,6,7,8,12,13],[2,5,6,8,10,13,14],[2,6,7,9,10,11,12],[3,4,5,6,9,10,13],[3,4,6,9,10,12,13],[3,4,7,8,10,12,14],[3,4,7,8,11,12,13],[3,5,7,9,11,13,14],[4,5,6,8,10,11,14]];
G[62]:=Group([(1,2)(3,4)(6,9)(7,8)(10,13)(11,14),(1,7)(2,11)(3,9)(4,13)(6,10)(8,14)]);
# Design 63: autom. group order 6, simple, residual
B[63]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,7,10,11],[1,2,3,8,10,12,13],[1,2,4,9,11,12,14],[1,2,4,10,11,13,14],[1,3,5,6,9,13,14],[1,3,8,9,11,12,14],[1,4,5,6,11,12,13],[1,4,6,7,8,12,13],[1,5,7,8,9,10,12],[1,5,7,9,10,13,14],[1,6,7,8,10,11,14],[2,3,5,7,11,12,14],[2,3,6,9,10,12,13],[2,4,5,8,10,13,14],[2,4,6,7,8,9,14],[2,5,6,8,9,10,11],[2,5,7,8,11,12,13],[2,6,7,9,12,13,14],[3,4,5,7,10,12,14],[3,4,6,8,10,12,14],[3,4,7,8,9,11,13],[3,4,7,9,10,11,13],[3,5,6,8,11,13,14],[4,5,6,9,10,11,12]];
G[63]:=Group([(1,2,6,12,5,14)(3,9,4,7,13,11)]);
# Design 64: autom. group order 6, simple, residual
B[64]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,8,10,11],[1,2,3,10,11,12,13],[1,2,4,7,9,12,14],[1,2,4,10,12,13,14],[1,3,5,6,12,13,14],[1,3,7,9,10,11,14],[1,4,5,6,7,11,13],[1,4,6,8,9,10,14],[1,5,7,8,11,12,14],[1,5,8,9,11,12,13],[1,6,7,8,9,10,13],[2,3,5,8,9,13,14],[2,3,6,7,9,11,12],[2,4,5,9,10,11,13],[2,4,6,8,11,12,14],[2,5,6,7,10,13,14],[2,5,7,8,10,11,14],[2,6,7,8,9,12,13],[3,4,5,7,8,10,12],[3,4,6,8,11,13,14],[3,4,7,8,10,12,13],[3,4,7,9,11,13,14],[3,5,6,9,10,12,14],[4,5,6,9,10,11,12]];
G[64]:=Group([(1,2)(3,4)(6,9)(7,8)(10,12)(11,14),(1,6,14,2,9,11)(3,10,8,4,12,7)]);
# Design 65: autom. group order 6, simple, residual
B[65]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,10,11,12],[1,2,3,7,10,13,14],[1,2,4,8,10,11,13],[1,2,4,9,12,13,14],[1,3,5,6,11,12,14],[1,3,8,9,10,11,14],[1,4,5,7,10,12,14],[1,4,6,7,8,9,11],[1,5,6,7,8,12,13],[1,5,7,9,10,11,13],[1,6,8,9,12,13,14],[2,3,5,8,11,12,13],[2,3,6,7,8,9,14],[2,4,5,9,11,12,14],[2,4,6,7,11,13,14],[2,5,6,8,10,13,14],[2,5,7,8,9,10,12],[2,6,7,9,10,11,12],[3,4,5,6,9,10,13],[3,4,6,9,10,12,13],[3,4,7,8,10,12,14],[3,4,7,8,11,12,13],[3,5,7,9,11,13,14],[4,5,6,8,10,11,14]];
G[65]:=Group([(1,2)(3,4)(6,9)(7,8)(10,13)(11,14),(1,7)(2,11)(3,9)(4,13)(6,10)(8,14)]);
# Design 66: autom. group order 6, simple
B[66]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,8,10,11],[1,2,3,10,12,13,14],[1,2,4,7,9,12,13],[1,2,4,10,11,12,14],[1,3,5,9,10,13,14],[1,3,6,7,11,12,13],[1,4,5,6,8,13,14],[1,4,6,7,9,10,11],[1,5,7,8,10,11,13],[1,5,8,9,11,12,14],[1,6,7,8,9,12,14],[2,3,5,7,9,11,14],[2,3,6,8,9,12,13],[2,4,5,6,11,12,14],[2,4,8,9,10,11,13],[2,5,6,7,10,13,14],[2,5,7,8,11,12,13],[2,6,7,8,9,10,14],[3,4,5,7,8,10,12],[3,4,6,8,11,13,14],[3,4,7,8,10,12,14],[3,4,7,9,11,13,14],[3,5,6,9,10,11,12],[4,5,6,9,10,12,13]];
G[66]:=Group([(1,2)(3,4)(6,9)(7,8)(10,12)(11,13),(1,6,11)(2,9,13)(3,10,7)(4,12,8)]);
# Design 67: autom. group order 6, simple
B[67]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,6,8],[1,2,3,7,9,10,11],[1,2,3,9,10,12,13],[1,2,4,7,12,13,14],[1,2,4,9,11,12,14],[1,3,5,8,9,12,13],[1,3,7,8,11,13,14],[1,4,5,8,9,10,14],[1,4,6,8,10,11,13],[1,5,6,7,11,12,14],[1,5,6,10,11,12,13],[1,6,7,8,9,10,14],[2,3,5,8,11,13,14],[2,3,6,8,10,12,14],[2,4,6,8,9,11,12],[2,4,7,8,10,11,13],[2,5,6,7,9,10,13],[2,5,6,9,11,13,14],[2,5,7,8,10,12,14],[3,4,5,7,10,11,12],[3,4,5,9,10,11,14],[3,4,6,7,9,13,14],[3,4,6,10,12,13,14],[3,6,7,8,9,11,12],[4,5,7,8,9,12,13]];
G[67]:=Group([(1,2)(3,4)(5,6)(9,12)(10,14)(11,13),(1,3,6)(2,4,5)(9,14,11)(10,13,12)]);
# Design 68: autom. group order 6, simple, residual
B[68]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,6,8],[1,2,3,7,9,10,11],[1,2,3,9,10,11,12],[1,2,4,7,12,13,14],[1,2,4,9,12,13,14],[1,3,5,8,9,12,13],[1,3,7,8,10,13,14],[1,4,5,8,10,11,13],[1,4,6,8,9,10,14],[1,5,6,7,11,12,14],[1,5,6,10,11,12,14],[1,6,7,8,9,11,13],[2,3,5,8,10,12,14],[2,3,6,8,11,13,14],[2,4,6,8,9,11,12],[2,4,7,8,10,11,14],[2,5,6,7,9,10,13],[2,5,6,9,10,13,14],[2,5,7,8,11,12,13],[3,4,5,7,9,11,14],[3,4,5,9,11,13,14],[3,4,6,7,10,12,13],[3,4,6,10,11,12,13],[3,6,7,8,9,12,14],[4,5,7,8,9,10,12]];
G[68]:=Group([(1,2)(3,4)(5,6)(9,12)(10,14)(11,13),(1,3,6)(2,4,5)(9,13,14)(10,12,11)]);
# Design 69: autom. group order 6, simple, residual
B[69]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,6,8],[1,2,3,7,9,10,11],[1,2,3,9,12,13,14],[1,2,4,7,12,13,14],[1,2,4,9,10,11,12],[1,3,5,8,10,13,14],[1,3,7,8,10,11,13],[1,4,5,8,9,10,12],[1,4,6,8,9,11,14],[1,5,6,7,11,12,13],[1,5,6,9,10,13,14],[1,6,7,8,11,12,14],[2,3,5,8,11,12,14],[2,3,6,8,9,12,13],[2,4,6,8,10,11,13],[2,4,7,8,10,13,14],[2,5,6,7,9,10,14],[2,5,6,10,11,12,13],[2,5,7,8,9,11,14],[3,4,5,7,9,11,13],[3,4,5,10,11,12,14],[3,4,6,7,10,12,14],[3,4,6,9,11,13,14],[3,6,7,8,9,10,12],[4,5,7,8,9,12,13]];
G[69]:=Group([(1,2)(3,4)(5,6)(9,12)(10,13)(11,14),(1,3,6)(2,4,5)(9,14,13)(10,12,11)]);
# Design 70: autom. group order 6, simple
B[70]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,6,8],[1,2,3,7,9,10,11],[1,2,3,9,10,12,13],[1,2,4,7,12,13,14],[1,2,4,9,11,12,14],[1,3,5,8,10,13,14],[1,3,7,8,11,13,14],[1,4,5,8,9,11,13],[1,4,6,8,9,10,12],[1,5,6,7,11,12,14],[1,5,6,10,11,12,13],[1,6,7,8,9,10,14],[2,3,5,8,9,12,14],[2,3,6,8,11,12,13],[2,4,6,8,10,11,14],[2,4,7,8,10,11,13],[2,5,6,7,9,10,13],[2,5,6,9,11,13,14],[2,5,7,8,10,12,14],[3,4,5,7,10,11,12],[3,4,5,9,10,11,14],[3,4,6,7,9,13,14],[3,4,6,10,12,13,14],[3,6,7,8,9,11,12],[4,5,7,8,9,12,13]];
G[70]:=Group([(1,2)(3,4)(5,6)(9,12)(10,14)(11,13),(1,3,6)(2,4,5)(9,14,11)(10,13,12)]);
# Design 71: autom. group order 6, simple
B[71]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,6,8],[1,2,3,7,9,10,11],[1,2,3,9,10,12,13],[1,2,4,7,12,13,14],[1,2,4,9,11,12,14],[1,3,5,8,10,12,14],[1,3,7,8,10,11,14],[1,4,5,8,9,11,12],[1,4,6,8,10,11,13],[1,5,6,7,9,13,14],[1,5,6,10,12,13,14],[1,6,7,8,9,11,13],[2,3,5,8,11,13,14],[2,3,6,8,9,12,13],[2,4,6,8,9,10,14],[2,4,7,8,10,13,14],[2,5,6,7,10,11,12],[2,5,6,9,10,11,14],[2,5,7,8,11,12,13],[3,4,5,7,9,10,13],[3,4,5,9,11,13,14],[3,4,6,7,11,12,14],[3,4,6,10,11,12,13],[3,6,7,8,9,12,14],[4,5,7,8,9,10,12]];
G[71]:=Group([(1,2)(3,4)(5,6)(9,12)(10,14)(11,13),(1,3,6)(2,4,5)(9,11,14)(10,12,13)]);
# Design 72: autom. group order 6, simple
B[72]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,6,8],[1,2,3,7,9,10,11],[1,2,3,9,10,12,13],[1,2,4,7,12,13,14],[1,2,4,9,11,12,14],[1,3,5,8,11,12,13],[1,3,7,8,10,11,14],[1,4,5,8,10,11,14],[1,4,6,8,9,10,12],[1,5,6,7,9,13,14],[1,5,6,10,12,13,14],[1,6,7,8,9,11,13],[2,3,5,8,9,12,14],[2,3,6,8,10,13,14],[2,4,6,8,9,11,13],[2,4,7,8,10,13,14],[2,5,6,7,10,11,12],[2,5,6,9,10,11,14],[2,5,7,8,11,12,13],[3,4,5,7,9,10,13],[3,4,5,9,11,13,14],[3,4,6,7,11,12,14],[3,4,6,10,11,12,13],[3,6,7,8,9,12,14],[4,5,7,8,9,10,12]];
G[72]:=Group([(1,2)(3,4)(5,6)(9,12)(10,14)(11,13),(1,3,6)(2,4,5)(9,11,14)(10,12,13)]);
# Design 73: autom. group order 6, simple
B[73]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,10,11,12],[1,2,3,7,10,11,13],[1,2,4,6,12,13,14],[1,2,4,8,9,10,14],[1,3,5,7,8,12,14],[1,3,6,7,9,13,14],[1,4,5,10,12,13,14],[1,4,7,8,10,11,13],[1,5,6,9,11,12,13],[1,5,7,8,9,11,12],[1,6,8,9,10,11,14],[2,3,5,8,11,13,14],[2,3,8,9,10,12,13],[2,4,6,7,8,11,12],[2,4,7,9,11,12,14],[2,5,6,7,9,10,14],[2,5,6,8,11,13,14],[2,5,7,9,10,12,13],[3,4,5,6,9,10,11],[3,4,5,10,11,12,14],[3,4,6,8,9,12,13],[3,4,7,9,11,13,14],[3,6,7,8,10,12,14],[4,5,6,7,8,10,13]];
G[73]:=Group([(1,4,10)(2,5,11)(7,9,12)(8,14,13),(1,7)(2,14)(4,9)(5,13)(8,11)(10,12)]);
# Design 74: autom. group order 6, simple
B[74]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,8,10,11],[1,2,3,10,11,12,13],[1,2,4,6,7,12,14],[1,2,4,9,10,12,13],[1,3,5,8,12,13,14],[1,3,6,7,9,13,14],[1,4,5,8,9,10,14],[1,4,7,10,11,12,14],[1,5,6,7,9,11,13],[1,5,7,8,11,12,13],[1,6,8,9,10,11,14],[2,3,5,9,11,12,14],[2,3,7,9,10,13,14],[2,4,6,8,11,13,14],[2,4,7,8,9,11,13],[2,5,6,7,8,10,12],[2,5,6,9,11,12,14],[2,5,7,8,10,13,14],[3,4,5,6,10,11,13],[3,4,5,7,10,11,14],[3,4,6,8,12,13,14],[3,4,7,8,9,11,12],[3,6,7,8,9,10,12],[4,5,6,9,10,12,13]];
G[74]:=Group([(1,4,10)(2,5,11)(7,13,8)(9,14,12),(1,7)(2,9)(4,13)(5,14)(8,10)(11,12)]);
# Design 75: autom. group order 6, simple
B[75]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,10,11,12],[1,2,3,8,9,10,13],[1,2,4,6,7,11,14],[1,2,4,8,11,12,13],[1,3,5,10,11,12,14],[1,3,6,9,11,13,14],[1,4,5,7,10,13,14],[1,4,9,10,12,13,14],[1,5,6,7,8,10,13],[1,5,7,8,9,11,12],[1,6,7,8,9,12,14],[2,3,5,7,12,13,14],[2,3,7,8,12,13,14],[2,4,6,8,10,12,14],[2,4,7,9,10,11,13],[2,5,6,8,9,10,14],[2,5,6,9,11,13,14],[2,5,7,9,10,11,12],[3,4,5,6,9,12,13],[3,4,5,8,10,11,14],[3,4,6,7,9,10,12],[3,4,7,8,9,11,14],[3,6,7,8,10,11,13],[4,5,6,8,11,12,13]];
G[75]:=Group([(1,4,6,9,11,10)(2,12,14,7,3,13)]);
# Design 76: autom. group order 6, simple, residual
B[76]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,8,10,11],[1,2,3,10,11,12,13],[1,2,4,6,12,13,14],[1,2,4,7,9,10,14],[1,3,5,8,9,12,14],[1,3,6,7,8,13,14],[1,4,5,10,12,13,14],[1,4,8,9,10,11,13],[1,5,6,7,9,11,12],[1,5,7,8,11,12,13],[1,6,7,9,10,11,14],[2,3,5,9,11,13,14],[2,3,7,9,10,12,13],[2,4,6,8,11,12,14],[2,4,7,8,9,11,12],[2,5,6,7,8,10,13],[2,5,6,9,11,13,14],[2,5,7,8,10,12,14],[3,4,5,6,10,11,12],[3,4,5,7,10,11,14],[3,4,6,7,9,12,13],[3,4,7,8,11,13,14],[3,6,8,9,10,12,14],[4,5,6,8,9,10,13]];
G[76]:=Group([(1,4,10)(2,5,11)(7,12,8)(9,14,13),(1,7)(2,13)(4,8)(5,14)(9,11)(10,12)]);
# Design 77: autom. group order 6, simple
B[77]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,7,10,11],[1,2,3,8,10,11,12],[1,2,4,6,9,12,13],[1,2,4,10,12,13,14],[1,3,5,7,8,13,14],[1,3,8,11,12,13,14],[1,4,5,7,10,13,14],[1,4,6,8,9,11,14],[1,5,6,9,10,11,14],[1,5,7,9,10,11,12],[1,6,7,8,9,12,13],[2,3,5,9,11,13,14],[2,3,6,9,10,13,14],[2,4,7,8,9,11,14],[2,4,7,8,10,11,13],[2,5,6,7,8,12,14],[2,5,6,8,10,12,14],[2,5,7,9,11,12,13],[3,4,5,6,11,12,13],[3,4,5,8,9,10,12],[3,4,6,7,11,12,14],[3,4,7,9,10,12,14],[3,6,7,8,9,10,13],[4,5,6,8,10,11,13]];
G[77]:=Group([(1,3,4,11,9,13)(2,12,8,5,6,14)]);
# Design 78: autom. group order 6, simple
B[78]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,8,10,11],[1,2,3,9,10,12,13],[1,2,4,6,10,12,14],[1,2,4,7,11,12,14],[1,3,5,8,11,13,14],[1,3,7,9,10,13,14],[1,4,5,8,10,12,13],[1,4,7,8,11,13,14],[1,5,6,7,9,11,12],[1,5,6,9,11,12,13],[1,6,7,8,9,10,14],[2,3,5,6,7,13,14],[2,3,8,9,11,12,14],[2,4,6,8,9,11,13],[2,4,7,9,10,11,13],[2,5,6,10,11,13,14],[2,5,7,8,9,12,14],[2,5,7,8,10,12,13],[3,4,5,7,9,10,11],[3,4,5,10,11,12,14],[3,4,6,7,8,12,13],[3,4,6,9,12,13,14],[3,6,7,8,10,11,12],[4,5,6,8,9,10,14]];
G[78]:=Group([(1,5,11,6,9,12)(2,4,3,10,8,14)]);
# Design 79: autom. group order 6, simple, residual
B[79]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,10,11,12],[1,2,3,10,11,12,13],[1,2,4,7,8,10,14],[1,2,4,9,11,13,14],[1,3,5,7,8,11,13],[1,3,7,9,10,13,14],[1,4,5,6,10,12,14],[1,4,6,8,11,13,14],[1,5,6,7,9,12,13],[1,5,8,9,10,12,14],[1,6,7,8,9,11,12],[2,3,5,6,9,13,14],[2,3,6,8,9,12,14],[2,4,6,7,8,12,13],[2,4,7,9,10,12,13],[2,5,6,7,10,11,14],[2,5,7,8,9,10,11],[2,5,8,11,12,13,14],[3,4,5,7,11,12,14],[3,4,5,8,10,12,13],[3,4,6,8,9,10,11],[3,4,7,9,11,12,14],[3,6,7,8,10,13,14],[4,5,6,9,10,11,13]];
G[79]:=Group([(1,2,10)(3,11,12)(4,7,14),(1,4,2,7,10,14)(3,12,11)(5,13)(6,9)]);
# Design 80: autom. group order 6, simple, residual
B[80]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,10,11,12],[1,2,3,10,11,12,13],[1,2,4,7,8,10,14],[1,2,4,9,11,13,14],[1,3,5,7,8,12,13],[1,3,7,9,10,13,14],[1,4,5,6,10,12,14],[1,4,6,8,11,13,14],[1,5,6,7,9,11,13],[1,5,8,9,10,12,14],[1,6,7,8,9,11,12],[2,3,5,8,11,13,14],[2,3,6,8,9,12,14],[2,4,6,7,8,12,13],[2,4,7,9,10,12,13],[2,5,6,7,10,11,14],[2,5,6,9,12,13,14],[2,5,7,8,9,10,11],[3,4,5,6,9,10,13],[3,4,5,7,11,12,14],[3,4,6,8,9,10,11],[3,4,7,9,11,12,14],[3,6,7,8,10,13,14],[4,5,8,10,11,12,13]];
G[80]:=Group([(1,2,10)(3,11,12)(4,7,14),(1,4,2,7,10,14)(3,12,11)(5,13)(6,9)]);
# Design 81: autom. group order 6, simple
B[81]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,6,11,12],[1,2,3,8,9,10,11],[1,2,4,5,11,13,14],[1,2,4,8,12,13,14],[1,3,5,6,9,13,14],[1,3,7,10,12,13,14],[1,4,6,7,8,11,12],[1,4,6,7,9,10,13],[1,5,7,8,9,12,14],[1,5,7,8,10,11,14],[1,6,9,10,11,12,13],[2,3,6,7,9,12,14],[2,3,7,10,11,13,14],[2,4,5,9,10,12,14],[2,4,7,9,11,12,13],[2,5,6,7,8,10,13],[2,5,6,8,10,12,13],[2,6,7,8,9,11,14],[3,4,5,7,8,9,13],[3,4,5,7,10,11,12],[3,4,6,8,10,12,14],[3,4,6,8,11,13,14],[3,5,8,9,11,12,13],[4,5,6,9,10,11,14]];
G[81]:=Group([(1,3,9)(2,8,10)(5,13,6),(1,5,9,6,3,13)(2,8,10)(4,7)(11,12)]);
# Design 82: autom. group order 6, simple, residual
B[82]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,6,11,12],[1,2,3,8,11,13,14],[1,2,4,5,11,13,14],[1,2,4,8,9,10,12],[1,3,5,6,9,10,13],[1,3,7,8,12,13,14],[1,4,6,7,9,11,12],[1,4,6,7,10,13,14],[1,5,7,8,9,12,14],[1,5,7,9,10,11,14],[1,6,8,10,11,12,13],[2,3,6,7,10,12,14],[2,3,7,9,10,11,14],[2,4,5,9,12,13,14],[2,4,7,10,11,12,13],[2,5,6,7,8,9,13],[2,5,6,8,10,12,14],[2,6,7,8,9,11,13],[3,4,5,7,8,10,13],[3,4,5,7,8,11,12],[3,4,6,8,9,11,14],[3,4,6,9,12,13,14],[3,5,9,10,11,12,13],[4,5,6,8,10,11,14]];
G[82]:=Group([(1,4,10)(2,8,9)(6,7,13),(1,6)(3,5)(4,7)(10,13)(11,12)]);
# Design 83: autom. group order 6, simple, residual
B[83]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,6,8,11],[1,2,3,9,11,12,13],[1,2,4,5,12,13,14],[1,2,4,9,10,11,14],[1,3,5,6,10,12,14],[1,3,7,8,9,12,13],[1,4,6,7,8,11,13],[1,4,6,7,10,12,13],[1,5,7,8,9,10,14],[1,5,7,9,11,13,14],[1,6,8,10,11,12,14],[2,3,6,7,10,13,14],[2,3,7,10,11,13,14],[2,4,5,8,12,13,14],[2,4,7,8,10,11,12],[2,5,6,7,9,11,12],[2,5,6,8,9,10,13],[2,6,7,8,9,12,14],[3,4,5,7,8,11,14],[3,4,5,7,9,10,12],[3,4,6,8,9,13,14],[3,4,6,9,11,12,14],[3,5,8,10,11,12,13],[4,5,6,9,10,11,13]];
G[83]:=Group([(2,13,14)(3,7,10)(4,12,5),(1,6)(3,5)(4,7)(8,11)(10,12)]);
# Design 84: autom. group order 6, simple, residual
B[84]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,6,8,11],[1,2,3,11,12,13,14],[1,2,4,5,9,10,12],[1,2,4,11,12,13,14],[1,3,5,6,9,13,14],[1,3,7,8,10,12,13],[1,4,6,7,8,11,13],[1,4,6,7,9,12,14],[1,5,7,8,10,12,14],[1,5,7,9,10,11,13],[1,6,8,9,10,11,14],[2,3,6,7,10,12,14],[2,3,7,9,10,11,13],[2,4,5,8,10,13,14],[2,4,7,8,9,11,14],[2,5,6,7,10,11,14],[2,5,6,8,9,12,13],[2,6,7,8,9,12,13],[3,4,5,7,8,11,12],[3,4,5,7,9,13,14],[3,4,6,8,10,13,14],[3,4,6,9,10,11,12],[3,5,8,9,11,12,14],[4,5,6,10,11,12,13]];
G[84]:=Group([(1,6)(3,5)(4,7)(8,11)(9,14),(1,8,14,6,11,9)(2,12,13)(3,5)(4,7)]);
# Design 85: autom. group order 6, simple, residual
B[85]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,11,13,14],[1,2,4,5,9,13,14],[1,2,4,7,11,12,13],[1,3,5,6,9,10,13],[1,3,6,7,8,9,12],[1,4,6,8,10,12,14],[1,4,6,10,11,12,14],[1,5,7,8,10,13,14],[1,5,7,9,10,11,12],[1,7,8,9,11,13,14],[2,3,7,9,10,12,14],[2,3,7,10,12,13,14],[2,4,5,7,8,10,11],[2,4,6,7,8,9,14],[2,5,6,8,10,12,13],[2,5,6,9,11,12,14],[2,6,8,9,10,11,13],[3,4,5,8,12,13,14],[3,4,5,9,10,11,14],[3,4,6,7,10,11,13],[3,4,8,9,11,12,13],[3,5,6,7,8,11,14],[4,5,6,7,9,12,13]];
G[85]:=Group([(1,2,4,7,6,3)(8,13)(9,11)(10,12,14)]);
# Design 86: autom. group order 6, simple, residual
B[86]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,11,13,14],[1,2,4,5,9,13,14],[1,2,4,7,11,12,13],[1,3,5,6,9,10,13],[1,3,6,7,8,9,12],[1,4,6,8,10,12,14],[1,4,6,10,11,12,14],[1,5,7,8,10,12,13],[1,5,7,9,10,11,14],[1,7,8,9,11,13,14],[2,3,7,9,10,12,14],[2,3,7,10,12,13,14],[2,4,5,7,8,10,11],[2,4,6,7,8,9,14],[2,5,6,8,12,13,14],[2,5,6,9,10,11,12],[2,6,8,9,10,11,13],[3,4,5,8,10,13,14],[3,4,5,9,11,12,14],[3,4,6,7,10,11,13],[3,4,8,9,11,12,13],[3,5,6,7,8,11,14],[4,5,6,7,9,12,13]];
G[86]:=Group([(1,2,4,7,6,3)(8,13)(9,11)(10,12,14)]);
# Design 87: autom. group order 6, simple, residual
B[87]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,6,11,13,14],[1,2,4,5,9,13,14],[1,2,4,7,8,12,13],[1,3,5,9,10,11,14],[1,3,6,7,10,11,12],[1,4,6,7,9,10,14],[1,4,6,8,10,11,13],[1,5,6,7,12,13,14],[1,5,7,8,9,10,12],[1,8,9,11,12,13,14],[2,3,6,9,10,12,13],[2,3,7,8,10,13,14],[2,4,5,6,9,11,12],[2,4,7,10,11,12,14],[2,5,6,8,10,12,14],[2,5,7,9,10,11,13],[2,6,7,8,9,11,14],[3,4,5,7,8,11,14],[3,4,5,10,12,13,14],[3,4,6,8,9,12,14],[3,4,7,9,11,12,13],[3,5,6,7,8,9,13],[4,5,6,8,10,11,13]];
G[87]:=Group([(2,3)(4,11)(6,8)(7,12)(9,14)(10,13),(2,7,14)(3,12,9)(4,6,13)(8,10,11)]);
# Design 88: autom. group order 6, simple, residual
B[88]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,11,12,13],[1,2,3,6,8,9,11],[1,2,4,5,10,12,14],[1,2,4,7,11,13,14],[1,3,5,7,8,12,14],[1,3,6,9,12,13,14],[1,4,6,7,9,10,13],[1,4,7,8,10,11,12],[1,5,6,9,10,11,12],[1,5,7,8,9,13,14],[1,6,8,10,11,13,14],[2,3,6,7,10,12,13],[2,3,7,9,10,11,14],[2,4,5,6,8,9,14],[2,4,9,11,12,13,14],[2,5,6,7,8,11,13],[2,5,8,9,10,12,13],[2,6,7,8,10,12,14],[3,4,5,6,10,13,14],[3,4,5,8,10,11,13],[3,4,6,8,11,12,14],[3,4,7,8,9,12,13],[3,5,7,9,10,11,14],[4,5,6,7,9,11,12]];
G[88]:=Group([(1,4)(3,14)(6,12)(7,10)(8,13)(9,11),(1,6,13)(3,7,11)(4,8,12)(9,10,14)]);
# Design 89: autom. group order 6, simple, residual
B[89]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,11,12,13],[1,2,3,6,8,9,11],[1,2,4,5,10,12,14],[1,2,4,7,11,13,14],[1,3,5,8,10,13,14],[1,3,6,9,12,13,14],[1,4,6,7,9,10,13],[1,4,7,8,10,11,12],[1,5,6,7,9,12,14],[1,5,7,8,9,11,12],[1,6,8,10,11,13,14],[2,3,6,7,10,12,13],[2,3,7,9,10,11,14],[2,4,5,6,8,9,14],[2,4,9,11,12,13,14],[2,5,6,7,8,11,13],[2,5,8,9,10,12,13],[2,6,7,8,10,12,14],[3,4,5,6,10,11,12],[3,4,5,7,8,13,14],[3,4,6,8,11,12,14],[3,4,7,8,9,12,13],[3,5,7,9,10,11,14],[4,5,6,9,10,11,13]];
G[89]:=Group([(1,4)(3,14)(6,12)(7,10)(8,13)(9,11),(1,6,13)(3,7,11)(4,8,12)(9,10,14)]);
# Design 90: autom. group order 6, simple, residual
B[90]:=[[1,2,3,4,5,6,7],[1,2,3,4,8,9,10],[1,2,3,5,8,11,12],[1,2,3,9,11,13,14],[1,2,4,5,6,7,13],[1,2,4,10,11,12,14],[1,3,5,9,10,12,13],[1,3,6,7,8,10,14],[1,4,6,8,9,11,14],[1,4,7,8,9,12,13],[1,5,6,8,12,13,14],[1,5,7,10,11,13,14],[1,6,7,9,10,11,12],[2,3,6,7,11,12,14],[2,3,6,8,10,12,13],[2,4,6,9,12,13,14],[2,4,7,8,10,11,13],[2,5,6,9,10,11,13],[2,5,7,8,9,10,14],[2,5,7,8,9,12,14],[3,4,5,6,9,10,14],[3,4,5,7,9,11,12],[3,4,5,8,11,13,14],[3,4,7,10,12,13,14],[3,6,7,8,9,11,13],[4,5,6,8,10,11,12]];
G[90]:=Group([(1,4,6)(2,5,7)(8,9,14),(1,8)(2,5)(3,12)(4,14)(6,9)(10,13)]);
# Design 91: autom. group order 6, simple, residual
B[91]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,6,8],[1,2,3,7,9,10,11],[1,2,3,9,12,13,14],[1,2,4,10,11,12,13],[1,2,5,8,10,11,14],[1,3,4,8,10,12,14],[1,3,5,7,11,13,14],[1,4,6,7,9,10,12],[1,4,6,9,11,13,14],[1,5,6,8,9,10,13],[1,5,7,8,9,12,14],[1,6,7,8,11,12,13],[2,3,6,8,9,11,13],[2,3,7,8,10,12,13],[2,4,5,7,9,11,12],[2,4,5,9,10,13,14],[2,4,6,8,11,12,14],[2,5,6,7,12,13,14],[2,6,7,8,9,10,14],[3,4,5,8,9,12,13],[3,4,6,7,10,13,14],[3,4,7,8,9,11,14],[3,5,6,9,10,11,12],[3,5,6,10,11,12,14],[4,5,7,8,10,11,13]];
G[91]:=Group([(1,2,4)(3,5,6)(10,11,12),(1,10)(2,12)(4,11)(5,6)(7,14)(8,9)]);
# Design 92: autom. group order 6, simple
B[92]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,7,10,11],[1,2,3,8,10,12,13],[1,2,4,6,11,12,14],[1,2,5,10,12,13,14],[1,3,4,9,11,13,14],[1,3,5,8,11,13,14],[1,4,7,8,9,10,12],[1,4,7,9,11,12,13],[1,5,6,7,8,9,14],[1,5,6,9,10,12,14],[1,6,7,8,10,11,13],[2,3,6,8,9,12,13],[2,3,7,9,10,11,14],[2,4,5,7,10,13,14],[2,4,5,8,9,10,11],[2,4,6,8,11,12,14],[2,5,7,9,11,12,13],[2,6,7,8,9,13,14],[3,4,5,6,7,12,13],[3,4,6,9,10,13,14],[3,4,7,8,10,12,14],[3,5,6,9,10,11,12],[3,5,7,8,11,12,14],[4,5,6,8,10,11,13]];
G[92]:=Group([(2,4,12)(3,9,10)(5,7,13)(6,11,14),(2,6)(3,7)(4,11)(5,10)(9,13)(12,14)]);
# Design 93: autom. group order 6, simple
B[93]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,8,10,11],[1,2,3,10,12,13,14],[1,2,4,6,9,12,13],[1,2,5,7,10,11,12],[1,3,4,8,11,13,14],[1,3,6,7,11,12,14],[1,4,5,7,9,11,14],[1,4,5,10,12,13,14],[1,5,8,9,10,11,13],[1,6,7,8,9,10,12],[1,6,7,8,9,13,14],[2,3,5,8,9,12,14],[2,3,7,9,10,13,14],[2,4,6,9,11,12,13],[2,4,7,8,10,11,13],[2,4,7,8,11,12,14],[2,5,6,7,8,13,14],[2,5,6,9,10,11,14],[3,4,5,6,7,10,13],[3,4,6,9,10,11,14],[3,4,7,8,9,10,12],[3,5,6,8,11,12,13],[3,5,7,9,11,12,13],[4,5,6,8,10,12,14]];
G[93]:=Group([(2,4)(3,5)(6,9)(7,8)(10,14)(12,13),(2,6,12)(3,7,10)(4,9,13)(5,8,14)]);
# Design 94: autom. group order 6, simple
B[94]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,8,10,11],[1,2,3,10,12,13,14],[1,2,4,6,9,12,13],[1,2,5,8,11,12,14],[1,3,4,7,10,11,13],[1,3,8,9,11,13,14],[1,4,5,7,9,11,14],[1,4,5,10,12,13,14],[1,5,6,7,10,11,12],[1,6,7,8,9,10,13],[1,6,7,8,9,12,14],[2,3,5,6,7,13,14],[2,3,7,9,10,12,14],[2,4,6,9,11,12,13],[2,4,7,8,10,11,12],[2,4,7,8,11,13,14],[2,5,6,9,10,11,14],[2,5,7,8,9,10,13],[3,4,5,8,9,10,12],[3,4,6,7,8,12,14],[3,4,6,9,10,11,14],[3,5,6,8,11,12,13],[3,5,7,9,11,12,13],[4,5,6,8,10,13,14]];
G[94]:=Group([(2,4)(3,5)(6,9)(7,8)(10,14)(12,13),(2,6,12)(3,7,14)(4,9,13)(5,8,10)]);
# Design 95: autom. group order 6, simple, residual
B[95]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,8,10,11],[1,2,3,7,10,12,13],[1,2,4,6,9,12,14],[1,2,5,11,12,13,14],[1,3,4,11,12,13,14],[1,3,7,9,10,11,14],[1,4,5,7,9,10,13],[1,4,5,8,10,11,14],[1,5,6,8,10,12,13],[1,6,7,8,9,11,12],[1,6,7,8,9,13,14],[2,3,5,8,9,13,14],[2,3,6,9,10,11,13],[2,4,6,9,10,12,14],[2,4,7,8,10,11,14],[2,4,7,8,10,12,13],[2,5,6,7,11,13,14],[2,5,7,8,9,11,12],[3,4,5,6,7,11,12],[3,4,6,7,8,13,14],[3,4,8,9,11,12,13],[3,5,6,8,10,12,14],[3,5,7,9,10,12,14],[4,5,6,9,10,11,13]];
G[95]:=Group([(2,4)(3,5)(6,9)(7,8)(11,13)(12,14),(2,6,12)(3,8,13)(4,9,14)(5,7,11)]);
# Design 96: autom. group order 6, simple, residual
B[96]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,6,8],[1,2,3,9,10,11,12],[1,2,3,9,10,11,13],[1,2,4,7,9,12,14],[1,2,5,8,10,13,14],[1,3,4,8,9,13,14],[1,3,6,7,11,12,14],[1,4,5,7,9,11,13],[1,4,6,10,12,13,14],[1,5,6,8,10,11,12],[1,5,7,8,11,12,13],[1,6,7,8,9,10,14],[2,3,5,7,10,12,14],[2,3,6,8,11,13,14],[2,4,5,11,12,13,14],[2,4,6,8,9,11,12],[2,4,7,8,10,11,14],[2,5,6,7,9,10,13],[2,6,7,8,9,12,13],[3,4,5,8,9,10,12],[3,4,6,7,10,11,13],[3,4,7,8,10,12,13],[3,5,6,9,12,13,14],[3,5,7,8,9,11,14],[4,5,6,9,10,11,14]];
G[96]:=Group([(2,3)(4,9)(5,11)(6,10)(7,13)(8,12),(1,2)(4,10)(5,9)(6,11)(7,13)(8,12)]);
# Design 97: autom. group order 6, simple, residual
B[97]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,6,8],[1,2,3,9,10,11,12],[1,2,3,9,10,11,13],[1,2,4,7,9,12,14],[1,2,5,8,10,13,14],[1,3,4,8,9,13,14],[1,3,6,7,11,12,14],[1,4,5,11,12,13,14],[1,4,6,7,9,10,13],[1,5,6,8,10,11,12],[1,5,7,8,9,11,14],[1,6,7,8,10,12,13],[2,3,5,7,10,12,14],[2,3,6,8,11,13,14],[2,4,5,7,10,11,13],[2,4,6,8,9,11,12],[2,4,7,8,11,12,13],[2,5,6,9,12,13,14],[2,6,7,8,9,10,14],[3,4,5,8,9,10,12],[3,4,6,10,12,13,14],[3,4,7,8,10,11,14],[3,5,6,7,9,11,13],[3,5,7,8,9,12,13],[4,5,6,9,10,11,14]];
G[97]:=Group([(2,3)(4,9)(5,11)(6,10)(7,13)(8,12),(1,2)(4,10)(5,9)(6,11)(7,13)(8,12)]);
# Design 98: autom. group order 6, simple, residual
B[98]:=[[1,2,3,4,5,6,7],[1,2,3,4,5,8,9],[1,2,3,6,10,11,12],[1,2,3,10,11,13,14],[1,2,4,6,8,12,13],[1,2,5,7,10,13,14],[1,3,4,9,12,13,14],[1,3,7,8,9,11,13],[1,4,5,6,11,12,14],[1,4,7,8,9,10,14],[1,5,6,8,9,11,14],[1,5,7,8,10,11,12],[1,6,7,9,10,12,13],[2,3,5,8,9,10,12],[2,3,6,7,9,11,14],[2,4,5,9,10,11,13],[2,4,7,8,11,12,13],[2,4,7,9,11,12,14],[2,5,6,7,8,13,14],[2,6,8,9,10,12,14],[3,4,5,7,10,12,14],[3,4,6,7,8,10,11],[3,4,6,8,10,13,14],[3,5,6,7,9,12,13],[3,5,8,11,12,13,14],[4,5,6,9,10,11,13]];
G[98]:=Group([(1,3)(4,11)(5,10)(7,12)(8,14)(9,13),(1,7,8)(3,14,12)(4,5,13)(9,10,11)]);