D:=[]; G:=[]; R:=[]; RG:=[]; # Design 1: 11 resolution(s), autom. group order 1920, simple D[1]:=[[1,2,3,4],[1,2,5,6],[1,3,7,8],[1,4,9,10],[1,5,11,12],[1,6,13,14],[1,7,11,15],[1,8,13,16],[1,9,12,16],[1,10,14,15],[2,3,11,13],[2,4,12,14],[2,5,7,9],[2,6,8,10],[2,7,11,16],[2,8,13,15],[2,9,12,15],[2,10,14,16],[3,4,15,16],[3,5,7,10],[3,5,11,14],[3,6,8,9],[3,6,12,13],[3,9,14,16],[3,10,12,15],[4,5,8,9],[4,5,12,13],[4,6,7,10],[4,6,11,14],[4,7,13,15],[4,8,11,16],[5,6,15,16],[5,8,14,15],[5,10,13,16],[6,7,12,16],[6,9,11,15],[7,8,12,14],[7,9,13,14],[8,10,11,12],[9,10,11,13]]; G[1]:=Group([(5,6)(7,8)(9,10)(11,13)(12,14)(15,16),(3,4)(7,9)(8,10)(11,12)(13,14)(15,16),(3,5)(4,6)(7,11)(8,12)(9,13)(10,14),(2,3)(5,7)(6,8)(9,10)(12,15)(14,16),(1,2)(7,11)(8,13)(9,12)(10,14)(15,16)]); R[1]:=[]; RG[1]:=[]; # Design 1 / Resolution 1: autom. group order 1920 R[1][1]:=[[1,32,37,40],[2,19,38,39],[3,12,34,36],[4,11,33,35],[5,14,24,30],[6,13,25,31],[7,18,22,27],[8,17,20,29],[9,16,21,28],[10,15,23,26]]; RG[1][1]:=Group([(5,6)(7,8)(9,10)(11,13)(12,14)(15,16),(3,4)(7,9)(8,10)(11,12)(13,14)(15,16),(3,5)(4,6)(7,11)(8,12)(9,13)(10,14),(2,3)(5,8)(6,7)(11,13)(12,16)(14,15),(1,2)(7,11)(8,13)(9,12)(10,14)(15,16)]); # Design 1 / Resolution 2: autom. group order 128 R[1][2]:=[[1,32,37,40],[2,19,38,39],[3,12,34,36],[4,11,33,35],[5,14,24,30],[6,13,25,31],[7,18,23,26],[8,17,20,29],[9,16,21,28],[10,15,22,27]]; RG[1][2]:=Group([(3,4)(5,6)(7,10)(8,9)(11,14)(12,13),(3,5)(4,6)(7,11)(8,12)(9,13)(10,14),(2,16)(3,8)(4,13)(5,12)(6,9)(10,14),(1,2)(7,11)(8,13)(9,12)(10,14)(15,16),(1,3)(2,4)(5,16)(6,15)(7,8)(9,11)(10,13)(12,14)]); # Design 1 / Resolution 3: autom. group order 128 R[1][3]:=[[1,32,37,40],[2,19,38,39],[3,12,34,36],[4,11,33,35],[5,14,24,30],[6,13,25,31],[7,18,23,26],[8,17,21,28],[9,16,20,29],[10,15,22,27]]; RG[1][3]:=Group([(5,6)(7,8)(9,10)(11,13)(12,14)(15,16),(3,4)(7,9)(8,10)(11,12)(13,14)(15,16),(3,5)(4,6)(7,11)(8,12)(9,13)(10,14),(1,2)(7,11)(8,13)(9,12)(10,14)(15,16),(1,3)(2,4)(5,16)(6,15)(7,8)(9,11)(10,13)(12,14),(1,8)(2,12)(3,7)(4,14)(5,10)(6,11)(9,15)(13,16)]); # Design 1 / Resolution 4: autom. group order 384 R[1][4]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,11,33,35],[5,14,24,30],[6,13,25,31],[7,18,23,26],[8,17,21,28],[9,16,20,29],[10,15,22,27]]; RG[1][4]:=Group([(5,6)(7,8)(9,10)(11,13)(12,14)(15,16),(3,4)(7,9)(8,10)(11,12)(13,14)(15,16),(3,5)(4,6)(7,11)(8,12)(9,13)(10,14),(2,16)(3,8)(4,13)(5,12)(6,9)(10,14),(1,2)(7,11)(8,13)(9,12)(10,14)(15,16),(1,3)(2,4)(5,15)(6,16)(9,13)(10,11)]); # Design 1 / Resolution 5: autom. group order 32 R[1][5]:=[[1,32,37,40],[2,19,38,39],[3,12,34,36],[4,11,33,35],[5,14,24,30],[6,15,25,26],[7,18,22,27],[8,17,21,28],[9,16,20,29],[10,13,23,31]]; RG[1][5]:=Group([(2,3)(5,7)(6,8)(9,10)(12,15)(14,16),(1,2)(3,4)(5,6)(7,14)(8,12)(9,13)(10,11)(15,16),(1,5)(2,6)(3,16)(4,15)(7,13)(8,10)(9,14)(11,12)]); # Design 1 / Resolution 6: autom. group order 32 R[1][6]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,11,33,35],[5,14,24,30],[6,15,25,26],[7,18,22,27],[8,17,21,28],[9,16,20,29],[10,13,23,31]]; RG[1][6]:=Group([(2,16)(3,12)(4,9)(5,8)(6,13)(7,11),(1,2)(3,4)(5,6)(7,14)(8,12)(9,13)(10,11)(15,16),(1,3)(2,4)(5,16)(6,15)(7,8)(9,11)(10,13)(12,14)]); # Design 1 / Resolution 7: autom. group order 96 R[1][7]:=[[1,32,37,40],[2,19,38,39],[3,12,34,36],[4,11,33,35],[5,18,22,30],[6,15,25,26],[7,14,24,27],[8,17,21,28],[9,16,20,29],[10,13,23,31]]; RG[1][7]:=Group([(3,4)(5,6)(7,10)(8,9)(11,14)(12,13),(2,3)(5,7)(6,8)(9,10)(12,15)(14,16),(1,2)(7,11)(8,13)(9,12)(10,14)(15,16),(1,5,2,6)(3,15,4,16)(7,8,14,12)(9,10,13,11)]); # Design 1 / Resolution 8: autom. group order 32 R[1][8]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,11,33,35],[5,18,22,30],[6,15,25,26],[7,14,24,27],[8,17,20,29],[9,16,21,28],[10,13,23,31]]; RG[1][8]:=Group([(3,4)(5,6)(7,10)(8,9)(11,14)(12,13),(1,2)(7,11)(8,13)(9,12)(10,14)(15,16),(1,3)(2,4)(5,16)(6,15)(7,8)(9,11)(10,13)(12,14),(1,5)(2,6)(3,16)(4,15)(7,13)(8,10)(9,14)(11,12),(1,8)(2,12)(3,7)(4,14)(5,10)(6,11)(9,15)(13,16)]); # 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],[5,18,22,30],[6,15,25,26],[7,14,24,27],[8,17,21,28],[9,16,20,29],[10,13,23,31]]; RG[1][9]:=Group([(3,4)(5,6)(7,10)(8,9)(11,14)(12,13),(1,2)(7,11)(8,13)(9,12)(10,14)(15,16),(1,3)(2,4)(5,16)(6,15)(7,8)(9,11)(10,13)(12,14),(1,5)(2,6)(3,16)(4,15)(7,13)(8,10)(9,14)(11,12),(1,8)(2,12)(3,7)(4,14)(5,10)(6,11)(9,15)(13,16)]); # Design 1 / Resolution 10: autom. group order 64 R[1][10]:=[[1,32,38,39],[2,19,37,40],[3,12,34,36],[4,15,23,33],[5,16,24,28],[6,17,20,31],[7,18,22,27],[8,13,25,29],[9,14,21,30],[10,11,26,35]]; RG[1][10]:=Group([(2,12,13,10)(3,11,8,15)(4,5,16,14)(6,9),(1,2)(3,4)(5,6)(7,14)(8,12)(9,13)(10,11)(15,16)]); # Design 1 / Resolution 11: autom. group order 320 R[1][11]:=[[1,32,38,39],[2,19,37,40],[3,18,27,36],[4,15,23,33],[5,16,24,28],[6,17,20,31],[7,12,22,34],[8,13,25,29],[9,14,21,30],[10,11,26,35]]; RG[1][11]:=Group([(3,4)(5,6)(7,10)(8,9)(11,14)(12,13),(3,5,4,6)(7,12,10,13)(8,11,9,14)(15,16),(2,13,10,7,12)(3,16,4,8,9)(5,6,14,15,11),(1,2)(7,11)(8,13)(9,12)(10,14)(15,16)]);