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