D:=[]; G:=[]; R:=[]; RG:=[]; # Design 1: 24 resolution(s), autom. group order 384, simple, decomposable D[1]:=[[1,2,3,4],[1,2,5,6],[1,3,7,8],[1,4,9,10],[1,5,7,9],[1,6,11,12],[1,8,13,14],[1,10,15,16],[1,11,13,15],[1,12,14,16],[2,3,11,14],[2,4,12,15],[2,5,8,10],[2,6,14,15],[2,7,10,16],[2,7,11,13],[2,8,9,13],[2,9,12,16],[3,4,13,16],[3,5,10,15],[3,5,12,14],[3,6,7,10],[3,6,9,12],[3,8,11,16],[3,9,13,15],[4,5,8,14],[4,5,11,15],[4,6,7,11],[4,6,8,9],[4,7,14,16],[4,10,12,13],[5,6,13,16],[5,7,12,13],[5,9,11,16],[6,8,15,16],[6,10,13,14],[7,8,12,15],[7,9,14,15],[8,10,11,12],[9,10,11,14]]; G[1]:=Group([(3,4)(7,9)(8,10)(11,12)(13,16)(14,15),(2,3)(5,7)(6,8)(11,14)(12,13)(15,16),(2,5)(3,7)(4,9)(11,12)(13,14)(15,16),(2,11)(3,13)(4,15)(5,12)(7,14)(9,16),(1,2)(5,6)(7,14)(8,11)(9,15)(10,12)]); R[1]:=[]; RG[1]:=[]; # Design 1 / Resolution 1: autom. group order 384, decomposable R[1][1]:=[[1,32,37,40],[2,19,38,39],[3,12,34,36],[4,11,33,35],[5,14,24,31],[6,13,25,30],[7,18,22,27],[8,16,21,29],[9,15,23,26],[10,17,20,28]]; RG[1][1]:=Group([(3,4)(7,9)(8,10)(11,12)(13,16)(14,15),(2,3)(5,7)(6,8)(11,14)(12,13)(15,16),(2,5)(3,7)(4,9)(11,12)(13,14)(15,16),(2,16,3,12,4,14)(5,15,7,11,9,13)(6,10,8),(1,2)(5,6)(7,14)(8,11)(9,15)(10,12)]); # Design 1 / Resolution 2: autom. group order 32 R[1][2]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,11,33,35],[5,14,24,31],[6,13,25,30],[7,18,22,27],[8,16,21,29],[9,15,23,26],[10,17,20,28]]; RG[1][2]:=Group([(3,4)(7,9)(8,10)(11,12)(13,16)(14,15),(1,2)(5,6)(7,14)(8,11)(9,15)(10,12),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15),(1,5)(2,6)(3,16)(4,13)(7,9)(8,11)(10,12)(14,15),(1,7)(2,15)(3,8)(4,12)(5,9)(6,14)(10,13)(11,16)]); # Design 1 / Resolution 3: autom. group order 16 R[1][3]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,11,33,35],[5,14,24,31],[6,13,25,30],[7,15,23,27],[8,16,21,29],[9,18,22,26],[10,17,20,28]]; RG[1][3]:=Group([(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15),(1,5)(2,6)(3,16)(4,13)(7,9)(8,11)(10,12)(14,15),(1,7)(2,15)(3,8)(4,12)(5,9)(6,14)(10,13)(11,16)]); # Design 1 / Resolution 4: autom. group order 32 R[1][4]:=[[1,32,37,40],[2,19,38,39],[3,12,34,36],[4,11,33,35],[5,14,24,31],[6,13,25,30],[7,15,23,27],[8,17,21,28],[9,18,22,26],[10,16,20,29]]; RG[1][4]:=Group([(3,4)(7,9)(8,10)(11,12)(13,16)(14,15),(1,2)(5,6)(7,14)(8,11)(9,15)(10,12),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15),(1,5)(2,6)(3,16)(4,13)(7,9)(8,11)(10,12)(14,15),(1,7)(2,15)(3,8)(4,12)(5,9)(6,14)(10,13)(11,16)]); # Design 1 / Resolution 5: autom. group order 32 R[1][5]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,11,33,35],[5,14,24,31],[6,13,25,30],[7,15,23,27],[8,17,21,28],[9,18,22,26],[10,16,20,29]]; RG[1][5]:=Group([(3,4)(7,9)(8,10)(11,12)(13,16)(14,15),(1,2)(5,6)(7,14)(8,11)(9,15)(10,12),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15),(1,5)(2,6)(3,16)(4,13)(7,9)(8,11)(10,12)(14,15),(1,7)(2,15)(3,8)(4,12)(5,9)(6,14)(10,13)(11,16)]); # Design 1 / Resolution 6: autom. group order 128 R[1][6]:=[[1,32,37,40],[2,19,38,39],[3,18,27,36],[4,11,33,35],[5,14,24,31],[6,13,25,30],[7,12,22,34],[8,16,21,29],[9,15,23,26],[10,17,20,28]]; RG[1][6]:=Group([(2,5)(3,7)(4,9)(11,12)(13,14)(15,16),(2,11)(3,13)(4,15)(5,12)(7,14)(9,16),(2,4)(5,9)(6,10)(11,16)(12,15)(13,14),(1,6)(3,14)(4,15)(7,13)(8,10)(9,16),(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16)]); # Design 1 / Resolution 7: autom. group order 128 R[1][7]:=[[1,32,37,40],[2,19,38,39],[3,18,27,36],[4,16,21,35],[5,14,24,31],[6,13,25,30],[7,12,22,34],[8,11,29,33],[9,15,23,26],[10,17,20,28]]; RG[1][7]:=Group([(3,4)(7,9)(8,10)(11,12)(13,16)(14,15),(2,5)(3,9)(4,7)(8,10)(13,15)(14,16),(2,11)(3,13)(4,15)(5,12)(7,14)(9,16),(1,6)(3,14)(4,15)(7,13)(8,10)(9,16),(1,2)(5,6)(7,14)(8,11)(9,15)(10,12),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15)]); # Design 1 / Resolution 8: autom. group order 384 R[1][8]:=[[1,32,37,40],[2,25,30,39],[3,18,27,36],[4,16,21,35],[5,14,24,31],[6,13,19,38],[7,12,22,34],[8,11,29,33],[9,15,23,26],[10,17,20,28]]; RG[1][8]:=Group([(3,4)(7,9)(8,10)(11,12)(13,16)(14,15),(2,5)(3,9)(4,7)(8,10)(13,15)(14,16),(2,11)(3,13)(4,15)(5,12)(7,14)(9,16),(2,9)(3,7)(4,5)(6,10)(11,15)(12,16),(1,6)(3,14)(4,15)(7,13)(8,10)(9,16),(1,2)(5,6)(7,14)(8,11)(9,15)(10,12)]); # Design 1 / Resolution 9: autom. group order 32 R[1][9]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,11,33,35],[5,14,24,31],[6,13,25,30],[7,18,20,28],[8,16,23,26],[9,15,21,29],[10,17,22,27]]; RG[1][9]:=Group([(3,4)(7,9)(8,10)(11,12)(13,16)(14,15),(1,2)(5,6)(7,14)(8,11)(9,15)(10,12),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15),(1,5)(2,6)(3,16)(4,13)(7,9)(8,11)(10,12)(14,15),(1,7)(2,15)(3,8)(4,12)(5,9)(6,14)(10,13)(11,16)]); # Design 1 / Resolution 10: autom. group order 32 R[1][10]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,11,33,35],[5,14,24,31],[6,15,25,26],[7,18,22,27],[8,16,21,29],[9,13,23,30],[10,17,20,28]]; RG[1][10]:=Group([(2,11)(3,13)(4,15)(5,12)(7,14)(9,16),(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15)]); # Design 1 / Resolution 11: autom. group order 16 R[1][11]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,11,33,35],[5,14,24,31],[6,15,25,26],[7,18,22,27],[8,17,21,28],[9,13,23,30],[10,16,20,29]]; RG[1][11]:=Group([(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15),(1,5)(2,6)(3,16)(4,13)(7,9)(8,11)(10,12)(14,15),(1,7)(2,15)(3,8)(4,12)(5,9)(6,14)(10,13)(11,16)]); # Design 1 / Resolution 12: autom. group order 16 R[1][12]:=[[1,32,37,40],[2,19,38,39],[3,12,34,36],[4,16,21,35],[5,14,24,31],[6,13,25,30],[7,18,20,28],[8,11,29,33],[9,15,23,26],[10,17,22,27]]; RG[1][12]:=Group([(1,6)(2,5)(3,13)(4,16)(7,14)(8,10)(9,15)(11,12),(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,11)(2,10)(3,9)(4,14)(5,8)(6,12)(7,16)(13,15),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15)]); # Design 1 / Resolution 13: autom. group order 32 R[1][13]:=[[1,32,37,40],[2,25,30,39],[3,12,34,36],[4,16,21,35],[5,14,24,31],[6,13,19,38],[7,18,20,28],[8,11,29,33],[9,15,23,26],[10,17,22,27]]; RG[1][13]:=Group([(2,9)(3,7)(4,5)(6,10)(11,15)(12,16),(1,6)(2,5)(3,13)(4,16)(7,14)(8,10)(9,15)(11,12),(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16)]); # Design 1 / Resolution 14: autom. group order 16 R[1][14]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,16,21,35],[5,14,24,31],[6,13,25,30],[7,15,23,27],[8,11,29,33],[9,18,22,26],[10,17,20,28]]; RG[1][14]:=Group([(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,6)(2,5)(3,13)(4,16)(7,14)(8,10)(9,15)(11,12),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15),(1,11)(2,10)(3,9)(4,14)(5,8)(6,12)(7,16)(13,15)]); # Design 1 / Resolution 15: autom. group order 16 R[1][15]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,11,33,35],[5,14,24,31],[6,15,25,26],[7,18,20,28],[8,16,21,29],[9,13,23,30],[10,17,22,27]]; RG[1][15]:=Group([(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15),(1,5)(2,6)(3,16)(4,13)(7,9)(8,11)(10,12)(14,15),(1,7)(2,15)(3,8)(4,12)(5,9)(6,14)(10,13)(11,16)]); # Design 1 / Resolution 16: autom. group order 32 R[1][16]:=[[1,32,37,40],[2,25,30,39],[3,12,34,36],[4,11,33,35],[5,14,24,31],[6,13,19,38],[7,15,23,27],[8,17,21,28],[9,18,22,26],[10,16,20,29]]; RG[1][16]:=Group([(3,4)(7,9)(8,10)(11,12)(13,16)(14,15),(1,6)(2,5)(3,16)(4,13)(7,15)(9,14),(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,11)(2,10)(3,9)(4,14)(5,8)(6,12)(7,16)(13,15),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15)]); # Design 1 / Resolution 17: autom. group order 16 R[1][17]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,14,24,33],[5,11,31,35],[6,13,25,30],[7,15,23,27],[8,17,21,28],[9,18,22,26],[10,16,20,29]]; RG[1][17]:=Group([(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15),(1,5)(2,6)(3,16)(4,13)(7,9)(8,11)(10,12)(14,15),(1,7)(2,15)(3,8)(4,12)(5,9)(6,14)(10,13)(11,16)]); # Design 1 / Resolution 18: autom. group order 32 R[1][18]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,14,24,33],[5,11,31,35],[6,15,25,26],[7,18,22,27],[8,17,21,28],[9,13,23,30],[10,16,20,29]]; RG[1][18]:=Group([(2,11)(3,13)(4,15)(5,12)(7,14)(9,16),(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15)]); # Design 1 / Resolution 19: autom. group order 32 R[1][19]:=[[1,32,37,40],[2,19,38,39],[3,14,31,34],[4,16,21,35],[5,12,24,36],[6,13,25,30],[7,15,23,27],[8,11,29,33],[9,18,22,26],[10,17,20,28]]; RG[1][19]:=Group([(2,12)(3,14)(4,16)(5,11)(7,13)(9,15),(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,6)(2,5)(3,13)(4,16)(7,14)(8,10)(9,15)(11,12),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15)]); # Design 1 / Resolution 20: autom. group order 16 R[1][20]:=[[1,32,38,39],[2,19,37,40],[3,14,31,34],[4,16,21,35],[5,12,24,36],[6,13,25,30],[7,15,23,27],[8,11,29,33],[9,18,22,26],[10,17,20,28]]; RG[1][20]:=Group([(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,6)(2,5)(3,13)(4,16)(7,14)(8,10)(9,15)(11,12),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15),(1,11)(2,10)(3,9)(4,14)(5,8)(6,12)(7,16)(13,15)]); # Design 1 / Resolution 21: autom. group order 32 R[1][21]:=[[1,32,37,40],[2,19,38,39],[3,14,31,34],[4,16,21,35],[5,12,24,36],[6,13,25,30],[7,18,20,28],[8,11,29,33],[9,15,23,26],[10,17,22,27]]; RG[1][21]:=Group([(2,11)(3,13)(4,15)(5,12)(7,14)(9,16),(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,6)(2,5)(3,13)(4,16)(7,14)(8,10)(9,15)(11,12),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15)]); # Design 1 / Resolution 22: autom. group order 16 R[1][22]:=[[1,32,38,39],[2,19,37,40],[3,14,31,34],[4,16,21,35],[5,12,24,36],[6,13,25,30],[7,18,20,28],[8,11,29,33],[9,15,23,26],[10,17,22,27]]; RG[1][22]:=Group([(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,6)(2,5)(3,13)(4,16)(7,14)(8,10)(9,15)(11,12),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15),(1,11)(2,10)(3,9)(4,14)(5,8)(6,12)(7,16)(13,15)]); # Design 1 / Resolution 23: autom. group order 32 R[1][23]:=[[1,32,37,40],[2,25,30,39],[3,14,31,34],[4,16,21,35],[5,12,24,36],[6,13,19,38],[7,15,23,27],[8,11,29,33],[9,18,22,26],[10,17,20,28]]; RG[1][23]:=Group([(2,12)(3,14)(4,16)(5,11)(7,13)(9,15),(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,6)(2,5)(3,13)(4,16)(7,14)(8,10)(9,15)(11,12),(1,3,10,14)(2,15,11,16)(4,5,9,12)(6,13,8,7)]); # Design 1 / Resolution 24: autom. group order 32 R[1][24]:=[[1,32,38,39],[2,19,37,40],[3,18,27,36],[4,14,24,33],[5,11,31,35],[6,15,25,26],[7,12,22,34],[8,17,21,28],[9,13,23,30],[10,16,20,29]]; RG[1][24]:=Group([(2,11)(3,13)(4,15)(5,12)(7,14)(9,16),(1,2)(3,4)(5,6)(7,15)(8,12)(9,14)(10,11)(13,16),(1,5)(2,6)(3,16)(4,13)(7,9)(8,11)(10,12)(14,15),(1,3)(2,4)(5,16)(6,13)(7,8)(9,11)(10,14)(12,15)]); # Design 2: 3 resolution(s), autom. group order 384, decomposable D[2]:=[[1,2,3,4],[1,2,3,4],[1,5,6,7],[1,5,6,8],[1,7,9,10],[1,8,9,10],[1,11,12,13],[1,11,12,14],[1,13,15,16],[1,14,15,16],[2,5,7,11],[2,5,8,11],[2,6,12,13],[2,6,12,14],[2,7,9,15],[2,8,9,15],[2,10,13,16],[2,10,14,16],[3,5,13,15],[3,5,14,15],[3,6,7,16],[3,6,8,16],[3,7,10,12],[3,8,10,12],[3,9,11,13],[3,9,11,14],[4,5,10,13],[4,5,10,14],[4,6,9,13],[4,6,9,14],[4,7,11,16],[4,7,12,15],[4,8,11,16],[4,8,12,15],[5,9,12,16],[5,9,12,16],[6,10,11,15],[6,10,11,15],[7,8,13,14],[7,8,13,14]]; G[2]:=Group([(13,14),(7,8),(5,9)(6,10)(11,15)(12,16),(5,12)(6,11)(7,13)(8,14)(9,16)(10,15),(2,3)(5,6)(9,10)(11,16)(12,15),(1,2)(3,4)(6,11)(10,15),(1,5)(2,9)(3,16)(4,12)(10,11)]); R[2]:=[]; RG[2]:=[]; # Design 2 / Resolution 1: autom. group order 192, decomposable R[2][1]:=[[1,35,37,39],[2,36,38,40],[3,17,26,34],[4,18,25,32],[5,13,20,33],[6,14,19,31],[7,15,22,28],[8,16,21,27],[9,11,24,30],[10,12,23,29]]; RG[2][1]:=Group([(7,8)(13,14),(5,16)(6,15)(7,13)(8,14)(9,12)(10,11),(5,9)(6,10)(11,15)(12,16),(2,3)(5,6)(9,10)(11,16)(12,15)(13,14),(1,4)(5,10,9,6)(7,13,8,14)(11,16,15,12),(1,2)(3,4)(5,12)(7,13)(8,14)(9,16),(1,6,5)(2,10,16)(3,11,9)(4,15,12)]); # Design 2 / Resolution 2: autom. group order 48 R[2][2]:=[[1,35,37,39],[2,36,38,40],[3,17,26,34],[4,18,25,32],[5,13,20,33],[6,14,19,31],[7,16,21,28],[8,15,22,27],[9,11,24,30],[10,12,23,29]]; RG[2][2]:=Group([(7,8)(13,14),(2,3)(5,10)(6,9)(7,8)(11,12)(15,16),(1,4)(5,11)(6,16)(9,15)(10,12)(13,14),(1,2)(3,4)(5,16)(6,10)(7,13)(8,14)(9,12)(11,15),(1,6,12,3,11,16)(2,10,9,4,15,5)(7,13)(8,14)]); # Design 2 / Resolution 3: autom. group order 64 R[2][3]:=[[1,35,37,39],[2,36,38,40],[3,17,26,34],[4,18,25,32],[5,14,19,33],[6,13,20,31],[7,16,21,28],[8,15,22,27],[9,11,24,30],[10,12,23,29]]; RG[2][3]:=Group([(7,8)(13,14),(5,16)(6,15)(7,13)(8,14)(9,12)(10,11),(5,9)(6,10)(11,15)(12,16)(13,14),(1,4)(2,3)(5,9)(7,13)(8,14)(12,16),(1,2)(3,4)(5,12)(7,13,8,14)(9,16),(1,6)(2,11)(3,10)(4,15)(9,16)(13,14)]);