# Design 1: 1 resolution(s), autom. group order 6, simple D1:=[[1,2,3],[1,2,4],[1,3,5],[1,4,5],[1,6,7],[1,6,8],[1,7,9],[1,8,9],[2,3,6],[2,4,6],[2,5,7],[2,5,9],[2,7,8],[2,8,9],[3,4,8],[3,4,9],[3,5,7],[3,6,9],[3,7,8],[4,5,8],[4,6,7],[4,7,9],[5,6,8],[5,6,9]]; G1:=Group([(2,7)(3,9)(4,6)(5,8),(1,2)(3,4)(5,6)(8,9)]); R1_1:=[[1,22,23],[2,19,24],[3,14,21],[4,13,18],[5,12,15],[6,11,16],[7,9,20],[8,10,17]]; RG1_1:=Group([(2,7)(3,9)(4,6)(5,8),(1,2,7)(3,8,6)(4,5,9)]); # Design 2: 1 resolution(s), autom. group order 4 D2:=[[1,2,3],[1,2,3],[1,4,5],[1,4,6],[1,5,7],[1,6,8],[1,7,9],[1,8,9],[2,4,5],[2,4,9],[2,5,6],[2,6,8],[2,7,8],[2,7,9],[3,4,8],[3,4,9],[3,5,7],[3,5,8],[3,6,7],[3,6,9],[4,6,7],[4,7,8],[5,6,9],[5,8,9]]; G2:=Group([(4,9)(5,7)(6,8),(1,2)(4,5)(7,9)]); R2_1:=[[1,21,24],[2,22,23],[3,13,20],[4,14,18],[5,12,16],[6,10,17],[7,11,15],[8,9,19]]; RG2_1:=Group([(4,9)(5,7)(6,8),(1,2)(4,7)(5,9)(6,8)]); # Design 3: 1 resolution(s), autom. group order 4 D3:=[[1,2,3],[1,2,3],[1,4,5],[1,4,5],[1,6,7],[1,6,8],[1,7,9],[1,8,9],[2,4,6],[2,4,7],[2,5,6],[2,5,8],[2,7,9],[2,8,9],[3,4,8],[3,4,9],[3,5,7],[3,5,9],[3,6,7],[3,6,8],[4,6,9],[4,7,8],[5,6,9],[5,7,8]]; G3:=Group([(4,5)(7,8),(2,3)(6,9)(7,8)]); R3_1:=[[1,21,24],[2,22,23],[3,13,20],[4,14,19],[5,12,16],[6,10,18],[7,11,15],[8,9,17]]; RG3_1:=Group([(4,5)(7,8),(2,3)(4,5)(6,9)]); # Design 4: 1 resolution(s), autom. group order 6 D4:=[[1,2,3],[1,2,3],[1,4,5],[1,4,5],[1,6,7],[1,6,8],[1,7,9],[1,8,9],[2,4,6],[2,4,6],[2,5,7],[2,5,9],[2,7,8],[2,8,9],[3,4,8],[3,4,9],[3,5,7],[3,5,8],[3,6,7],[3,6,9],[4,7,8],[4,7,9],[5,6,8],[5,6,9]]; G4:=Group([(2,4)(3,5)(7,8),(1,2)(5,6)(8,9)]); R4_1:=[[1,21,24],[2,22,23],[3,13,20],[4,14,19],[5,12,15],[6,11,16],[7,9,18],[8,10,17]]; RG4_1:=Group([(2,4)(3,5)(7,8),(1,2)(5,6)(8,9)]); # Design 5: 1 resolution(s), autom. group order 18, simple D5:=[[1,2,3],[1,2,4],[1,3,5],[1,4,6],[1,5,7],[1,6,8],[1,7,9],[1,8,9],[2,3,6],[2,4,5],[2,5,7],[2,6,9],[2,7,8],[2,8,9],[3,4,8],[3,4,9],[3,5,9],[3,6,7],[3,7,8],[4,5,8],[4,6,7],[4,7,9],[5,6,8],[5,6,9]]; G5:=Group([(2,5)(4,7)(6,9),(1,2)(3,4)(8,9),(1,3,8)(2,4,9)(5,7,6)]); R5_1:=[[1,22,23],[2,19,24],[3,14,21],[4,13,17],[5,12,15],[6,11,16],[7,9,20],[8,10,18]]; RG5_1:=Group([(2,5)(4,7)(6,9),(1,3,8)(2,4,9)(5,7,6),(1,2)(3,4)(8,9)]); # Design 6: 1 resolution(s), autom. group order 24 D6:=[[1,2,3],[1,2,3],[1,4,5],[1,4,5],[1,6,7],[1,6,7],[1,8,9],[1,8,9],[2,4,6],[2,4,6],[2,5,8],[2,5,9],[2,7,8],[2,7,9],[3,4,8],[3,4,9],[3,5,7],[3,5,7],[3,6,8],[3,6,9],[4,7,8],[4,7,9],[5,6,8],[5,6,9]]; G6:=Group([(8,9),(4,6)(5,7),(2,3)(4,5)(6,7),(2,4)(3,5)]); R6_1:=[[1,21,24],[2,22,23],[3,13,20],[4,14,19],[5,11,16],[6,12,15],[7,9,17],[8,10,18]]; RG6_1:=Group([(8,9),(4,6)(5,7),(2,4)(3,5),(2,3)(4,7)(5,6)]); # Design 7: 1 resolution(s), autom. group order 108 D7:=[[1,2,3],[1,2,3],[1,4,5],[1,4,6],[1,5,7],[1,6,8],[1,7,9],[1,8,9],[2,4,5],[2,4,9],[2,5,8],[2,6,7],[2,6,8],[2,7,9],[3,4,6],[3,4,9],[3,5,7],[3,5,8],[3,6,7],[3,8,9],[4,7,8],[4,7,8],[5,6,9],[5,6,9]]; G7:=Group([(4,5)(6,7)(8,9),(4,6)(5,8)(7,9),(2,3)(5,6)(7,8),(1,2)(6,9)(7,8),(1,4)(2,7)(3,8)]); R7_1:=[[1,21,23],[2,22,24],[3,12,20],[4,14,18],[5,13,16],[6,10,17],[7,11,15],[8,9,19]]; RG7_1:=Group([(4,7,8)(5,9,6),(4,6)(5,8)(7,9),(2,3)(5,6)(7,8),(1,2)(6,9)(7,8),(1,4)(2,7)(3,8)]); # Design 8: 1 resolution(s), autom. group order 432 D8:=[[1,2,3],[1,2,3],[1,4,5],[1,4,5],[1,6,7],[1,6,7],[1,8,9],[1,8,9],[2,4,6],[2,4,6],[2,5,8],[2,5,8],[2,7,9],[2,7,9],[3,4,9],[3,4,9],[3,5,7],[3,5,7],[3,6,8],[3,6,8],[4,7,8],[4,7,8],[5,6,9],[5,6,9]]; G8:=Group([(4,5)(6,8)(7,9),(4,6)(5,7)(8,9),(2,3)(6,9)(7,8),(2,4)(3,5)(8,9),(1,2)(5,6)(7,8)]); R8_1:=[[1,21,23],[2,22,24],[3,13,19],[4,14,20],[5,11,15],[6,12,16],[7,9,17],[8,10,18]]; RG8_1:=Group([(4,7,8)(5,6,9),(4,5)(6,8)(7,9),(2,3)(6,9)(7,8),(2,4)(3,5)(8,9),(1,2)(5,6)(7,8)]); # Design 9: 1 resolution(s), autom. group order 32 D9:=[[1,2,3],[1,2,3],[1,4,5],[1,4,5],[1,6,7],[1,6,7],[1,8,9],[1,8,9],[2,4,6],[2,4,8],[2,5,6],[2,5,9],[2,7,8],[2,7,9],[3,4,7],[3,4,8],[3,5,7],[3,5,9],[3,6,8],[3,6,9],[4,6,9],[4,7,9],[5,6,8],[5,7,8]]; G9:=Group([(4,5)(8,9),(4,8)(5,9)(6,7),(2,3)(6,7),(2,4)(3,5)(6,8)(7,9)]); R9_1:=[[1,21,24],[2,22,23],[3,13,20],[4,14,19],[5,10,18],[6,12,16],[7,9,17],[8,11,15]]; RG9_1:=Group([(4,9)(5,8)(6,7),(4,8)(5,9)(6,7),(2,3)(6,7),(2,4)(3,5)(6,8)(7,9)]);