Design No 1(for Input Group of Order 16 and Index 12) Group Size 32 20DCCD5A 66A4E80B Group generators (treatments are numbered () d c cd b bd bc bcd a ad ac acd ab abd abc abcd ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[2,3],[4,9],[5,8],[6,10],[7,11],[12,13],[16,17],[20,24],[21,25],[22,27],[23,26],[30,31],[34,35],[36,41],[37,40],[38,42],[39,43],[44,45],[48,61],[49,60],[50,62],[51,63],[54,55],[56,57]], [[0,1],[4,8],[5,9],[6,11],[7,10],[14,15],[18,19],[20,25],[21,24],[22,26],[23,27],[28,29],[32,33],[36,40],[37,41],[38,43],[39,42],[46,47],[48,60],[49,61],[50,63],[51,62],[52,53],[58,59]], [[0,2],[1,3],[4,6],[5,7],[8,10],[9,11],[12,14],[13,15],[16,18],[17,19],[20,22],[21,23],[24,26],[25,27],[28,30],[29,31],[32,34],[33,35],[36,38],[37,39],[40,42],[41,43],[44,46],[45,47],[48,50],[49,51],[52,54],[53,55],[56,58],[57,59],[60,62],[61,63]], [[0,4,1,5],[2,6,3,7],[8,12,9,13],[10,14,11,15],[16,20,17,21],[18,22,19,23],[24,28,25,29],[26,30,27,31],[32,36,33,37],[34,38,35,39],[40,44,41,45],[42,46,43,47],[48,52,49,53],[50,54,51,55],[56,60,57,61],[58,62,59,63]] Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^16 {(0)^3 (1)^22 (2)^18 (3)^4 (5)^1 }^16 {(0)^2 (1)^25 (2)^15 (3)^5 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc ac abc () c b ab abcd Design No 2(for Input Group of Order 16 and Index 12) Group Size 16 809DF397 51776782 Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^32 {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc ac abc () c b abd abc Design No 3(for Input Group of Order 16 and Index 12) Group Size 32 60186991 D6C6C67A Group generators (treatments are numbered () d c cd b bd bc bcd a ad ac acd ab abd abc abcd ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[2,3],[4,9],[5,8],[6,10],[7,11],[12,13],[16,17],[20,24],[21,25],[22,27],[23,26],[30,31],[34,35],[36,41],[37,40],[38,42],[39,43],[44,45],[48,61],[49,60],[50,62],[51,63],[54,55],[56,57]], [[0,1],[2,3],[4,5],[6,7],[8,9],[10,11],[12,13],[14,15],[16,17],[18,19],[20,21],[22,23],[24,25],[26,27],[28,29],[30,31],[32,33],[34,35],[36,37],[38,39],[40,41],[42,43],[44,45],[46,47],[48,49],[50,51],[52,53],[54,55],[56,57],[58,59],[60,61],[62,63]], [[0,2],[1,3],[4,6],[5,7],[8,10],[9,11],[12,14],[13,15],[16,18],[17,19],[20,22],[21,23],[24,26],[25,27],[28,30],[29,31],[32,34],[33,35],[36,38],[37,39],[40,42],[41,43],[44,46],[45,47],[48,50],[49,51],[52,54],[53,55],[56,58],[57,59],[60,62],[61,63]], [[0,4,1,5],[2,6,3,7],[8,12,9,13],[10,14,11,15],[16,20,17,21],[18,22,19,23],[24,28,25,29],[26,30,27,31],[32,36,33,37],[34,38,35,39],[40,44,41,45],[42,46,43,47],[48,52,49,53],[50,54,51,55],[56,60,57,61],[58,62,59,63]] Block Intersection Formula {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^32 Initial Blocks, in the group representation: () d c b a () d bc ac abc () c bd ab abcd Design No 4(for Input Group of Order 16 and Index 12) Group Size 16 FBDEDE08 E4B95613 Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^32 {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc ac abc () c a ab abcd Design No 5(for Input Group of Order 16 and Index 12) Group Size 32 BFCBD059 676E3D48 Group generators (treatments are numbered () d c cd b bd bc bcd a ad ac acd ab abd abc abcd ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[2,3],[4,9],[5,8],[6,10],[7,11],[12,13],[16,17],[20,24],[21,25],[22,27],[23,26],[30,31],[34,35],[36,41],[37,40],[38,42],[39,43],[44,45],[48,60],[49,61],[50,63],[51,62],[52,53],[58,59]], [[0,1],[2,3],[4,5],[6,7],[8,9],[10,11],[12,13],[14,15],[16,17],[18,19],[20,21],[22,23],[24,25],[26,27],[28,29],[30,31],[32,33],[34,35],[36,37],[38,39],[40,41],[42,43],[44,45],[46,47],[48,49],[50,51],[52,53],[54,55],[56,57],[58,59],[60,61],[62,63]], [[0,2],[1,3],[4,6],[5,7],[8,10],[9,11],[12,14],[13,15],[16,18],[17,19],[20,22],[21,23],[24,26],[25,27],[28,30],[29,31],[32,34],[33,35],[36,38],[37,39],[40,42],[41,43],[44,46],[45,47],[48,50],[49,51],[52,54],[53,55],[56,58],[57,59],[60,62],[61,63]], [[0,4,1,5],[2,6,3,7],[8,12,9,13],[10,14,11,15],[16,20,17,21],[18,22,19,23],[24,28,25,29],[26,30,27,31],[32,36,33,37],[34,38,35,39],[40,44,41,45],[42,46,43,47],[48,52,49,53],[50,54,51,55],[56,60,57,61],[58,62,59,63]] Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^32 {(0)^3 (1)^22 (2)^18 (3)^4 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc ac abc () c a abd abc Design No 6(for Input Group of Order 16 and Index 12) Group Size 32 2D50884F 803164A3 Group generators (treatments are numbered () d c cd b bd bc bcd a ad ac acd ab abd abc abcd ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[2,3],[4,9],[5,8],[6,10],[7,11],[12,13],[16,17],[20,24],[21,25],[22,27],[23,26],[30,31],[34,35],[36,41],[37,40],[38,42],[39,43],[44,45],[48,60],[49,61],[50,63],[51,62],[52,53],[58,59]], [[0,1],[2,3],[4,5],[6,7],[8,9],[10,11],[12,13],[14,15],[16,17],[18,19],[20,21],[22,23],[24,25],[26,27],[28,29],[30,31],[32,33],[34,35],[36,37],[38,39],[40,41],[42,43],[44,45],[46,47],[48,49],[50,51],[52,53],[54,55],[56,57],[58,59],[60,61],[62,63]], [[0,2],[1,3],[4,6],[5,7],[8,10],[9,11],[12,14],[13,15],[16,18],[17,19],[20,22],[21,23],[24,26],[25,27],[28,30],[29,31],[32,34],[33,35],[36,38],[37,39],[40,42],[41,43],[44,46],[45,47],[48,50],[49,51],[52,54],[53,55],[56,58],[57,59],[60,62],[61,63]], [[0,4,1,5],[2,6,3,7],[8,12,9,13],[10,14,11,15],[16,20,17,21],[18,22,19,23],[24,28,25,29],[26,30,27,31],[32,36,33,37],[34,38,35,39],[40,44,41,45],[42,46,43,47],[48,52,49,53],[50,54,51,55],[56,60,57,61],[58,62,59,63]] Block Intersection Formula {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 {(0)^3 (1)^22 (2)^18 (3)^4 (5)^1 }^32 Initial Blocks, in the group representation: () d c b a () d bc ac abc () c ad abd abc Design No 7(for Input Group of Order 16 and Index 12) Group Size 16 B41CE113 77188417 Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^32 {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc acd abc () c b ab abcd Design No 8(for Input Group of Order 16 and Index 12) Group Size 16 DA3413FE 8DEF42AA Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^32 {(0)^3 (1)^22 (2)^18 (3)^4 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc acd abc () c b abd abc Design No 9(for Input Group of Order 16 and Index 12) Group Size 16 AF8B911A A7949988 Block Intersection Formula {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^48 Initial Blocks, in the group representation: () d c b a () d bc acd abc () c bd ab abcd Design No 10(for Input Group of Order 16 and Index 12) Group Size 16 9F09ECEA 517E5994 Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^16 {(0)^3 (1)^22 (2)^18 (3)^4 (5)^1 }^16 {(0)^2 (1)^25 (2)^15 (3)^5 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc acd abc () c bd abd abc Design No 11(for Input Group of Order 16 and Index 12) Group Size 16 F9AC6DA9 A030678E Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^32 {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc ab abc () cd b ac abc Design No 12(for Input Group of Order 16 and Index 12) Group Size 16 2851C635 66E47B11 Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^16 {(0)^6 (1)^13 (2)^27 (3)^1 (5)^1 }^16 {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc ab abc () cd b ac abcd Design No 13(for Input Group of Order 16 and Index 12) Group Size 16 C82C7E29 3AF04D29 Block Intersection Formula {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^32 Initial Blocks, in the group representation: () d c b a () d bc ab abc () cd b acd abc Design No 14(for Input Group of Order 16 and Index 12) Group Size 16 E6C8ED7E 74B731D5 Block Intersection Formula {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^48 Initial Blocks, in the group representation: () d c b a () d bc ab abc () cd b acd abcd Design No 15(for Input Group of Order 16 and Index 12) Group Size 16 2D1EA6C4 1D8DBB3E Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^16 {(0)^6 (1)^13 (2)^27 (3)^1 (5)^1 }^16 {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc ab abc () cd bd ac abc Design No 16(for Input Group of Order 16 and Index 12) Group Size 16 36B5E11B 34505BDD Block Intersection Formula {(0)^3 (1)^22 (2)^18 (3)^4 (5)^1 }^32 {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc ab abc () cd bd ac abcd Design No 17(for Input Group of Order 16 and Index 12) Group Size 16 BD07B587 B2D984B0 Block Intersection Formula {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^48 Initial Blocks, in the group representation: () d c b a () d bc ab abc () cd bd acd abc Design No 18(for Input Group of Order 16 and Index 12) Group Size 16 FF55354E 0CF63605 Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^32 {(0)^3 (1)^22 (2)^18 (3)^4 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc ab abc () cd bd acd abcd Design No 19(for Input Group of Order 16 and Index 12) Group Size 16 B0F9B36B 5354AFEE Block Intersection Formula {(0)^3 (1)^22 (2)^18 (3)^4 (5)^1 }^32 {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc abd abc () c b ac abc Design No 20(for Input Group of Order 16 and Index 12) Group Size 16 751786FE 22F6EE15 Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^32 {(0)^3 (1)^22 (2)^18 (3)^4 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc abd abc () c b ac abcd Design No 21(for Input Group of Order 16 and Index 12) Group Size 16 AD738399 7AF7A904 Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^16 {(0)^6 (1)^13 (2)^27 (3)^1 (5)^1 }^16 {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc abd abc () c b acd abc Design No 22(for Input Group of Order 16 and Index 12) Group Size 16 78D03A34 C3626748 Block Intersection Formula {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^48 Initial Blocks, in the group representation: () d c b a () d bc abd abc () c b acd abcd Design No 23(for Input Group of Order 16 and Index 12) Group Size 16 BAAC13BA A29F887B Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^32 {(0)^3 (1)^22 (2)^18 (3)^4 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc abd abc () c bd ac abc Design No 24(for Input Group of Order 16 and Index 12) Group Size 16 8BE801FA 1EEBAF38 Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^32 {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 Initial Blocks, in the group representation: () d c b a () d bc abd abc () c bd ac abcd Design No 25(for Input Group of Order 16 and Index 12) Group Size 16 2C71E65C CB36A0C8 Block Intersection Formula {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^48 Initial Blocks, in the group representation: () d c b a () d bc abd abc () c bd acd abc Design No 26(for Input Group of Order 16 and Index 12) Group Size 16 50A91F27 178561AE Block Intersection Formula {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 {(0)^6 (1)^13 (2)^27 (3)^1 (5)^1 }^32 Initial Blocks, in the group representation: () d c b a () d bc abd abc () c bd acd abcd Design No 27(for Input Group of Order 16 and Index 12) Group Size 16 5D90FF3C 60141153 Block Intersection Formula {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^32 {(0)^2 (1)^24 (2)^18 (3)^2 (4)^1 (5)^1 }^16 Initial Blocks, in the group representation: () d b bc a () d ac ab abc () cd b a acd Design No 28(for Input Group of Order 16 and Index 12) Group Size 16 621A06EB 56292329 Block Intersection Formula {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^32 {(0)^3 (1)^22 (2)^18 (3)^4 (5)^1 }^16 Initial Blocks, in the group representation: () d b bc a () d ac ab abcd () c b a acd Design No 29(for Input Group of Order 16 and Index 12) Group Size 32 91810F26 D3D3A30A Group generators (treatments are numbered () d c cd b bd bc bcd a ad ac acd ab abd abc abcd ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[4,7],[5,6],[8,9],[10,11],[12,14],[13,15],[16,17],[18,19],[20,22],[21,23],[28,31],[29,30],[32,33],[34,35],[36,38],[37,39],[44,47],[45,46],[48,50],[49,51],[52,53],[54,55],[56,59],[57,58]], [[0,1],[2,3],[4,5],[6,7],[8,9],[10,11],[12,13],[14,15],[16,17],[18,19],[20,21],[22,23],[24,25],[26,27],[28,29],[30,31],[32,33],[34,35],[36,37],[38,39],[40,41],[42,43],[44,45],[46,47],[48,49],[50,51],[52,53],[54,55],[56,57],[58,59],[60,61],[62,63]], [[0,2],[1,3],[4,5],[6,7],[8,11],[9,10],[16,19],[17,18],[24,26],[25,27],[28,29],[30,31],[32,35],[33,34],[40,42],[41,43],[44,45],[46,47],[52,55],[53,54],[56,57],[58,59],[60,62],[61,63]], [[0,4,1,5],[2,6,3,7],[8,12,9,13],[10,14,11,15],[16,20,17,21],[18,22,19,23],[24,28,25,29],[26,30,27,31],[32,36,33,37],[34,38,35,39],[40,44,41,45],[42,46,43,47],[48,52,49,53],[50,54,51,55],[56,60,57,61],[58,62,59,63]], [[0,8,1,9],[2,10,3,11],[4,13,5,12],[6,15,7,14],[16,24,17,25],[18,26,19,27],[20,29,21,28],[22,31,23,30],[32,40,33,41],[34,42,35,43],[36,45,37,44],[38,47,39,46],[48,56,49,57],[50,58,51,59],[52,61,53,60],[54,63,55,62]] Block Intersection Formula {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 {(0)^6 (1)^13 (2)^27 (3)^1 (5)^1 }^16 {(0)^4 (1)^19 (2)^21 (3)^3 (5)^1 }^16 Initial Blocks, in the group representation: () d b bc a () d ac ab abcd () c a acd ab Design No 30(for Input Group of Order 16 and Index 12) Group Size 64 0DEEF8EC 2A3F2F5D Group generators (treatments are numbered () d c cd b bd bc bcd a ad ac acd ab abd abc abcd ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[4,7],[5,6],[8,9],[10,11],[12,14],[13,15],[16,17],[18,19],[20,22],[21,23],[28,31],[29,30],[32,33],[34,35],[36,38],[37,39],[44,47],[45,46],[48,50],[49,51],[52,53],[54,55],[56,59],[57,58]], [[2,3],[4,12,7,14],[5,13,6,15],[8,10,9,11],[16,32,17,33],[18,35,19,34],[20,44,22,47],[21,45,23,46],[24,42],[25,43],[26,41],[27,40],[28,39,31,37],[29,38,30,36],[48,58,50,57],[49,59,51,56],[52,55,53,54],[60,61]], [[0,1],[2,3],[4,5],[6,7],[8,9],[10,11],[12,13],[14,15],[16,17],[18,19],[20,21],[22,23],[24,25],[26,27],[28,29],[30,31],[32,33],[34,35],[36,37],[38,39],[40,41],[42,43],[44,45],[46,47],[48,49],[50,51],[52,53],[54,55],[56,57],[58,59],[60,61],[62,63]], [[0,2],[1,3],[4,5],[6,7],[8,11],[9,10],[16,19],[17,18],[24,26],[25,27],[28,29],[30,31],[32,35],[33,34],[40,42],[41,43],[44,45],[46,47],[52,55],[53,54],[56,57],[58,59],[60,62],[61,63]], [[0,4,1,5],[2,6,3,7],[8,12,9,13],[10,14,11,15],[16,20,17,21],[18,22,19,23],[24,28,25,29],[26,30,27,31],[32,36,33,37],[34,38,35,39],[40,44,41,45],[42,46,43,47],[48,52,49,53],[50,54,51,55],[56,60,57,61],[58,62,59,63]] Block Intersection Formula {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^32 {(0)^3 (1)^22 (2)^18 (3)^4 (5)^1 }^16 Initial Blocks, in the group representation: () d b bc a () d ac ab abcd () c a acd abc Design No 31(for Input Group of Order 16 and Index 12) Group Size 64 61D0992B 2428CD29 Group generators (treatments are numbered () d c cd b bd bc bcd a ad ac acd ab abd abc abcd ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[4,7],[5,6],[8,9],[10,11],[12,14],[13,15],[16,17],[18,19],[20,22],[21,23],[28,31],[29,30],[32,33],[34,35],[36,38],[37,39],[44,47],[45,46],[48,50],[49,51],[52,53],[54,55],[56,59],[57,58]], [[2,3],[4,12,7,14],[5,13,6,15],[8,10,9,11],[16,32,17,33],[18,35,19,34],[20,44,22,47],[21,45,23,46],[24,42],[25,43],[26,41],[27,40],[28,39,31,37],[29,38,30,36],[48,58,50,57],[49,59,51,56],[52,55,53,54],[60,61]], [[0,1],[2,3],[4,5],[6,7],[8,9],[10,11],[12,13],[14,15],[16,17],[18,19],[20,21],[22,23],[24,25],[26,27],[28,29],[30,31],[32,33],[34,35],[36,37],[38,39],[40,41],[42,43],[44,45],[46,47],[48,49],[50,51],[52,53],[54,55],[56,57],[58,59],[60,61],[62,63]], [[0,2],[1,3],[4,5],[6,7],[8,11],[9,10],[16,19],[17,18],[24,26],[25,27],[28,29],[30,31],[32,35],[33,34],[40,42],[41,43],[44,45],[46,47],[52,55],[53,54],[56,57],[58,59],[60,62],[61,63]], [[0,4,1,5],[2,6,3,7],[8,12,9,13],[10,14,11,15],[16,20,17,21],[18,22,19,23],[24,28,25,29],[26,30,27,31],[32,36,33,37],[34,38,35,39],[40,44,41,45],[42,46,43,47],[48,52,49,53],[50,54,51,55],[56,60,57,61],[58,62,59,63]] Block Intersection Formula {(0)^6 (1)^13 (2)^27 (3)^1 (5)^1 }^32 {(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^16 Initial Blocks, in the group representation: () d b bc a () d ac ab abcd () c a acd abcd