Design No 1(for Input Group of Order 12 and Index 5) Group Size 768 84D4B25D 4ED6D9DE Group generators (treatments are numbered () c b bc bb bbc a ac ab abc abb abbc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[21,22]], [[19,20]], [[23,24]], [[17,18]], [[15,16]], [[13,14]], [[0,1],[2,3],[4,5],[6,7],[8,9],[10,11],[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],[63,64]], [[0,2,4],[1,3,5],[6,8,10],[7,9,11],[13,15,17],[14,16,18],[19,21,23],[20,22,24],[25,27,29],[26,28,30],[31,33,35],[32,34,36],[37,39,41],[38,40,42],[43,45,47],[44,46,48],[49,51,53],[50,52,54],[55,57,59],[56,58,60]], [[0,6,1,7],[2,8,3,9],[4,10,5,11],[13,19],[14,20],[15,21],[16,22],[17,23],[18,24],[25,31,26,32],[27,33,28,34],[29,35,30,36],[37,43,38,44],[39,45,40,46],[41,47,42,48],[49,55,50,56],[51,57,52,58],[53,59,54,60],[61,63,62,64]] Block Intersection Formula {(0)^20 (1)^30 (3)^2 }^12 {(0)^21 (1)^27 (2)^3 (3)^1 }^40 Initial Blocks, in the group representation, last block PC(4): 1000 () c () b a () bc ac () bc abbc c bc bbc Design No 2(for Input Group of Order 12 and Index 5) Group Size 768 B8020701 32DB218A Group generators (treatments are numbered () c b bc bb bbc a ac ab abc abb abbc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[23,24]], [[21,22]], [[19,20]], [[17,18]], [[15,16]], [[13,14]], [[0,1],[2,3],[4,5],[6,7],[8,9],[10,11],[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],[63,64]], [[0,2,4],[1,3,5],[6,8,10],[7,9,11],[13,15,17],[14,16,18],[19,21,23],[20,22,24],[25,27,29],[26,28,30],[31,33,35],[32,34,36],[37,39,41],[38,40,42],[43,45,47],[44,46,48],[49,51,53],[50,52,54],[55,57,59],[56,58,60]], [[0,6,1,7],[2,8,3,9],[4,10,5,11],[13,19],[14,20],[15,21],[16,22],[17,23],[18,24],[25,31,26,32],[27,33,28,34],[29,35,30,36],[37,43,38,44],[39,45,40,46],[41,47,42,48],[49,55,50,56],[51,57,52,58],[53,59,54,60],[61,63,62,64]] Block Intersection Formula {(0)^20 (1)^30 (3)^2 }^12 {(0)^21 (1)^27 (2)^3 (3)^1 }^40 Initial Blocks, in the group representation, last block PC(4): 1000 () c () b a () bc abc () bc abbc c bc bbc Design No 3(for Input Group of Order 12 and Index 5) Group Size 768 E2ADA99D C6DA1019 Group generators (treatments are numbered () c b bc bb bbc a ac ab abc abb abbc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[19,20]], [[21,22]], [[17,18]], [[23,24]], [[15,16]], [[13,14]], [[0,1],[2,3],[4,5],[6,7],[8,9],[10,11],[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],[63,64]], [[0,2,4],[1,3,5],[6,8,10],[7,9,11],[13,15,17],[14,16,18],[19,21,23],[20,22,24],[25,27,29],[26,28,30],[31,33,35],[32,34,36],[37,39,41],[38,40,42],[43,45,47],[44,46,48],[49,51,53],[50,52,54],[55,57,59],[56,58,60]], [[0,6,1,7],[2,8,3,9],[4,10,5,11],[13,19],[14,20],[15,21],[16,22],[17,23],[18,24],[25,31,26,32],[27,33,28,34],[29,35,30,36],[37,43,38,44],[39,45,40,46],[41,47,42,48],[49,55,50,56],[51,57,52,58],[53,59,54,60],[61,63,62,64]] Block Intersection Formula {(0)^20 (1)^30 (3)^2 }^12 {(0)^21 (1)^27 (2)^3 (3)^1 }^40 Initial Blocks, in the group representation, last block PC(4): 1000 () c () b abb () bc a () bc ac c bc bbc Design No 4(for Input Group of Order 12 and Index 5) Group Size 15360 80E4A9CF AFD45B84 Group generators (treatments are numbered () c b bc bb bbc a ac ab abc abb abbc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[19,20]], [[21,22]], [[23,24]], [[17,18]], [[15,16]], [[13,14]], [[4,10],[5,11],[6,9],[7,8],[17,23],[18,24],[19,21],[20,22],[25,62],[26,61],[27,46],[28,45],[29,59],[30,60],[31,63],[32,64],[33,53],[34,54],[35,40],[36,39],[37,49],[38,50],[47,57],[48,58]], [[2,3],[4,6,10,9],[5,7,11,8],[17,19,23,21],[18,20,24,22],[25,49,62,37],[26,50,61,38],[27,35,46,40],[28,36,45,39],[29,54,59,34],[30,53,60,33],[31,47,63,57],[32,48,64,58],[41,43],[42,44],[51,56],[52,55]], [[2,4],[3,5],[8,10],[9,11],[15,17],[16,18],[21,23],[22,24],[25,29],[26,30],[31,35],[32,36],[37,54],[38,53],[39,52],[40,51],[41,50],[42,49],[43,60],[44,59],[45,58],[46,57],[47,56],[48,55]], [[0,1],[4,7,10,8],[5,6,11,9],[17,19,23,21],[18,20,24,22],[25,50,62,38],[26,49,61,37],[27,36,46,39],[28,35,45,40],[29,53,59,33],[30,54,60,34],[31,48,63,58],[32,47,64,57],[41,44],[42,43],[51,55],[52,56]], [[0,2],[1,3],[6,8],[7,9],[13,15],[14,16],[19,21],[20,22],[27,29],[28,30],[33,35],[34,36],[37,50],[38,49],[39,54],[40,53],[41,52],[42,51],[43,56],[44,55],[45,60],[46,59],[47,58],[48,57]] Block Intersection Formula {(0)^20 (1)^30 (3)^2 }^12 {(0)^21 (1)^27 (2)^3 (3)^1 }^40 Initial Blocks, in the group representation, last block PC(4): 1000 () c () b abb () bc a () bc abc c bc bbc Design No 5(for Input Group of Order 12 and Index 5) Group Size 1536 C9039295 77FCE5FE Group generators (treatments are numbered () c b bc bb bbc a ac ab abc abb abbc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[19,20]], [[21,22]], [[17,18]], [[23,24]], [[15,16]], [[13,14]], [[2,4],[3,5],[8,10],[9,11],[15,17],[16,18],[21,23],[22,24],[25,29],[26,30],[31,35],[32,36],[37,54],[38,53],[39,52],[40,51],[41,50],[42,49],[43,60],[44,59],[45,58],[46,57],[47,56],[48,55]], [[0,1],[2,3],[4,5],[6,7],[8,9],[10,11],[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],[63,64]], [[0,2],[1,3],[6,8],[7,9],[13,15],[14,16],[19,21],[20,22],[27,29],[28,30],[33,35],[34,36],[37,50],[38,49],[39,54],[40,53],[41,52],[42,51],[43,56],[44,55],[45,60],[46,59],[47,58],[48,57]], [[0,6,1,7],[2,8,3,9],[4,10,5,11],[13,19],[14,20],[15,21],[16,22],[17,23],[18,24],[25,31,26,32],[27,33,28,34],[29,35,30,36],[37,43,38,44],[39,45,40,46],[41,47,42,48],[49,55,50,56],[51,57,52,58],[53,59,54,60],[61,63,62,64]] Block Intersection Formula {(0)^20 (1)^30 (3)^2 }^12 {(0)^21 (1)^27 (2)^3 (3)^1 }^40 Initial Blocks, in the group representation, last block PC(4): 1000 () c () b abb () bc ac () bc ab c bc bbc Design No 6(for Input Group of Order 12 and Index 5) Group Size 144 8DCD50CD EFAE8B08 Group generators (treatments are numbered () c b bc bb bbc a ac ab abc abb abbc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[2,4],[3,5],[8,10],[9,11],[13,17],[14,18],[19,23],[20,24],[27,29],[28,30],[33,35],[34,36],[37,54],[38,53],[39,52],[40,51],[41,50],[42,49],[43,60],[44,59],[45,58],[46,57],[47,56],[48,55]], [[6,7],[8,9],[10,11],[19,20],[21,22],[23,24],[25,26],[27,28],[29,30],[37,49],[38,50],[39,51],[40,52],[41,53],[42,54],[43,56],[44,55],[45,58],[46,57],[47,60],[48,59],[63,64]], [[1,6],[3,8],[5,10],[14,19],[16,21],[18,23],[26,32],[28,34],[30,36],[37,54],[38,48],[39,50],[40,44],[41,52],[42,46],[43,58],[45,60],[47,56],[49,57],[51,59],[53,55],[61,64]], [[0,1],[2,3],[4,5],[13,14],[15,16],[17,18],[31,32],[33,34],[35,36],[37,50],[38,49],[39,52],[40,51],[41,54],[42,53],[43,55],[44,56],[45,57],[46,58],[47,59],[48,60],[61,62]], [[0,2],[1,3],[6,8],[7,9],[15,17],[16,18],[21,23],[22,24],[25,27],[26,28],[31,33],[32,34],[37,50],[38,49],[39,54],[40,53],[41,52],[42,51],[43,56],[44,55],[45,60],[46,59],[47,58],[48,57]] Block Intersection Formula {(0)^21 (1)^27 (2)^3 (3)^1 }^52 Initial Blocks, in the group representation, last block PC(4): 1000 () b () c a () bc abb () bc abbc c bc bbc Design No 7(for Input Group of Order 12 and Index 5) Group Size 72 640D10C0 CC57FC28 Group generators (treatments are numbered () c b bc bb bbc a ac ab abc abb abbc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[6,7],[8,9],[10,11],[19,20],[21,22],[23,24],[25,26],[27,28],[29,30],[37,49],[38,50],[39,51],[40,52],[41,53],[42,54],[43,56],[44,55],[45,58],[46,57],[47,60],[48,59],[63,64]], [[1,6],[3,8],[5,10],[14,19],[16,21],[18,23],[25,37],[26,55],[27,39],[28,57],[29,41],[30,59],[31,56],[32,38],[33,58],[34,40],[35,60],[36,42],[44,49],[46,51],[48,53],[61,64]], [[0,1],[2,3],[4,5],[13,14],[15,16],[17,18],[31,32],[33,34],[35,36],[37,50],[38,49],[39,52],[40,51],[41,54],[42,53],[43,55],[44,56],[45,57],[46,58],[47,59],[48,60],[61,62]], [[0,2,4],[1,3,5],[6,8,10],[7,9,11],[13,15,17],[14,16,18],[19,21,23],[20,22,24],[25,27,29],[26,28,30],[31,33,35],[32,34,36],[37,39,41],[38,40,42],[43,45,47],[44,46,48],[49,51,53],[50,52,54],[55,57,59],[56,58,60]] Block Intersection Formula {(0)^21 (1)^27 (2)^3 (3)^1 }^52 Initial Blocks, in the group representation, last block PC(4): 1000 () b () c ab () bc a () bc ac c bc bbc Design No 8(for Input Group of Order 12 and Index 5) Group Size 12 1E4474A4 86E70D09 Block Intersection Formula {(0)^21 (1)^27 (2)^3 (3)^1 }^52 Initial Blocks, in the group representation, last block PC(4): 1000 () b () c ab () bc a () bc abc c bc bbc Design No 9(for Input Group of Order 12 and Index 5) Group Size 24 84034AF8 2F845DFE Group generators (treatments are numbered () c b bc bb bbc a ac ab abc abb abbc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[6,7],[8,9],[10,11],[19,20],[21,22],[23,24],[25,26],[27,28],[29,30],[37,49],[38,50],[39,51],[40,52],[41,53],[42,54],[43,56],[44,55],[45,58],[46,57],[47,60],[48,59],[63,64]], [[0,1],[2,3],[4,5],[13,14],[15,16],[17,18],[31,32],[33,34],[35,36],[37,50],[38,49],[39,52],[40,51],[41,54],[42,53],[43,55],[44,56],[45,57],[46,58],[47,59],[48,60],[61,62]], [[0,2,4],[1,3,5],[6,8,10],[7,9,11],[13,15,17],[14,16,18],[19,21,23],[20,22,24],[25,27,29],[26,28,30],[31,33,35],[32,34,36],[37,39,41],[38,40,42],[43,45,47],[44,46,48],[49,51,53],[50,52,54],[55,57,59],[56,58,60]], [[0,6],[1,7],[2,8],[3,9],[4,10],[5,11],[13,19],[14,20],[15,21],[16,22],[17,23],[18,24],[25,32],[26,31],[27,34],[28,33],[29,36],[30,35],[37,55],[38,56],[39,57],[40,58],[41,59],[42,60],[43,49],[44,50],[45,51],[46,52],[47,53],[48,54],[61,63],[62,64]] Block Intersection Formula {(0)^21 (1)^27 (2)^3 (3)^1 }^52 Initial Blocks, in the group representation, last block PC(4): 1000 () b () c ab () bc ab () bc abc c bc bbc Design No 10(for Input Group of Order 12 and Index 5) Group Size 12 0BCA9884 4CAF2F63 Block Intersection Formula {(0)^21 (1)^27 (2)^3 (3)^1 }^52 Initial Blocks, in the group representation, last block PC(4): 1000 () bc () c ab () b a () bc a c bc bbc Design No 11(for Input Group of Order 12 and Index 5) Group Size 12 7074155A DA10D537 Block Intersection Formula {(0)^21 (1)^27 (2)^3 (3)^1 }^52 Initial Blocks, in the group representation, last block PC(4): 1000 () bc () c ab () b a () bc ab c bc bbc Design No 12(for Input Group of Order 12 and Index 5) Group Size 156 415370DE 670E30A2 Group generators (treatments are numbered () c b bc bb bbc a ac ab abc abb abbc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[1,2,6],[3,11,5],[4,9,8],[7,10,12],[13,48,54],[14,32,47],[15,31,35],[16,63,45],[17,44,64],[18,49,36],[19,56,39],[20,59,22],[21,30,58],[24,42,27],[25,62,55],[26,37,41],[28,60,61],[29,38,57],[33,52,46],[43,53,51]], [[1,3,4,10],[2,11,9,12],[5,8,7,6],[13,62,36,26],[14,28,46,22],[15,57,63,19],[16,39,35,38],[17,27,53,58],[18,37,48,55],[20,32,60,33],[21,44,24,51],[23,50,40,34],[25,49,41,54],[29,45,56,31],[30,64,42,43],[47,61,52,59]], [[0,1],[2,3],[4,5],[6,7],[8,9],[10,11],[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],[63,64]] Block Intersection Formula {(0)^21 (1)^27 (2)^3 (3)^1 }^52 Initial Blocks, in the group representation, last block PC(4): 1000 () bc () c ab () b ab () bc ac c bc bbc Design No 13(for Input Group of Order 12 and Index 5) Group Size 12 D068B4AD FE6A8AC5 Block Intersection Formula {(0)^21 (1)^27 (2)^3 (3)^1 }^52 Initial Blocks, in the group representation, last block PC(4): 1000 () bc () c ab () b ab () bc abc c bc bbc