Design No 1(for Input Group of Order 12 and Index 1) Group Size 294912 7A4064FF F1A7DE56 Group generators (treatments are numbered (1) c cc b bc bcc a ac acc ab abc abcc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[44,56]], [[43,55]], [[45,57]], [[41,53]], [[47,59]], [[39,51]], [[38,50]], [[46,58]], [[40,52]], [[37,49]], [[42,54]], [[48,60]], [[3,6,9],[4,7,10],[5,8,11],[16,20,23],[17,21,24],[18,19,22],[25,34,28],[26,35,29],[27,36,30],[37,48,42],[38,46,40],[39,47,41],[43,44,45],[49,60,54],[50,58,52],[51,59,53],[55,56,57],[62,63,64]], [[1,2],[4,5],[6,9],[7,11],[8,10],[13,15],[16,18],[19,23],[20,22],[21,24],[25,28],[26,30],[27,29],[32,33],[35,36],[37,42],[38,41],[39,40],[43,44],[46,47],[49,54],[50,53],[51,52],[55,56],[58,59],[63,64]], [[0,1],[3,4],[6,10],[7,9],[8,11],[14,15],[17,18],[19,24],[20,23],[21,22],[25,29],[26,28],[27,30],[31,32],[34,35],[37,40],[38,42],[39,41],[43,45],[46,48],[49,52],[50,54],[51,53],[55,57],[58,60],[63,64]], [[0,3],[1,4],[2,5],[6,9],[7,10],[8,11],[13,16],[14,17],[15,18],[19,22],[20,23],[21,24],[25,28],[26,29],[27,30],[31,34],[32,35],[33,36],[37,40],[38,41],[39,42],[43,46],[44,47],[45,48],[49,52],[50,53],[51,54],[55,58],[56,59],[57,60],[61,62],[63,64]] Block Intersection Formula {(0)^21 (1)^27 (2)^3 (3)^1 }^28 {(0)^20 (1)^30 (3)^2 }^24 Initial Blocks, in the group representation, last block PC(4): 1000 (1) c (1) b a (1) bc acc (1) bc acc (1) c cc Design No 2(for Input Group of Order 12 and Index 1) Group Size 144 8DCD50CD EFAE8B08 Group generators (treatments are numbered (1) c cc b bc bcc a ac acc ab abc abcc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[6,9],[7,10],[8,11],[19,22],[20,23],[21,24],[25,28],[26,29],[27,30],[37,49],[38,50],[39,51],[40,52],[41,53],[42,54],[43,58],[44,59],[45,60],[46,55],[47,56],[48,57],[63,64]], [[3,6],[4,7],[5,8],[16,20],[17,21],[18,19],[28,34],[29,35],[30,36],[37,54],[38,52],[39,53],[40,55],[41,56],[42,57],[43,60],[44,58],[45,59],[46,50],[47,51],[48,49],[62,63]], [[1,2],[4,5],[7,8],[10,11],[13,15],[16,18],[19,20],[22,23],[26,27],[29,30],[32,33],[35,36],[37,54],[38,53],[39,52],[40,51],[41,50],[42,49],[43,59],[44,58],[45,60],[46,56],[47,55],[48,57]], [[0,1],[3,4],[6,7],[9,10],[14,15],[17,18],[19,21],[22,24],[25,26],[28,29],[31,32],[34,35],[37,52],[38,54],[39,53],[40,49],[41,51],[42,50],[43,60],[44,59],[45,58],[46,57],[47,56],[48,55]], [[0,3],[1,4],[2,5],[13,16],[14,17],[15,18],[31,34],[32,35],[33,36],[37,52],[38,53],[39,54],[40,49],[41,50],[42,51],[43,55],[44,56],[45,57],[46,58],[47,59],[48,60],[61,62]] Block Intersection Formula {(0)^21 (1)^27 (2)^3 (3)^1 }^52 Initial Blocks, in the group representation, last block PC(4): 1000 (1) c (1) b a (1) bc acc (1) bc abcc (1) c cc Design No 3(for Input Group of Order 12 and Index 1) Group Size 768 D47CE2AD 909BF1EA Group generators (treatments are numbered (1) c cc b bc bcc a ac acc ab abc abcc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[20,23]], [[21,24]], [[15,18]], [[19,22]], [[14,17]], [[13,16]], [[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]], [[0,3],[1,4],[2,5],[6,9],[7,10],[8,11],[25,28],[26,29],[27,30],[31,34],[32,35],[33,36],[37,40],[38,41],[39,42],[43,46],[44,47],[45,48],[49,52],[50,53],[51,54],[55,58],[56,59],[57,60],[61,62],[63,64]], [[0,6,3,9],[1,8,4,11],[2,7,5,10],[13,19],[14,21],[15,20],[16,22],[17,24],[18,23],[25,31,28,34],[26,33,29,36],[27,32,30,35],[37,43,40,46],[38,45,41,48],[39,44,42,47],[49,55,52,58],[50,57,53,60],[51,56,54,59],[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 (1) b (1) c a (1) bc ac (1) bc acc (1) c cc Design No 4(for Input Group of Order 12 and Index 1) Group Size 15360 80E4A9CF AFD45B84 Group generators (treatments are numbered (1) c cc b bc bcc a ac acc ab abc abcc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[20,23]], [[21,24]], [[19,22]], [[15,18]], [[14,17]], [[13,16]], [[2,6],[5,9],[7,11],[8,10],[15,19],[18,22],[20,21],[23,24],[25,61],[26,55],[27,47],[28,62],[29,58],[30,44],[31,51],[32,41],[33,64],[34,54],[35,38],[36,63],[37,49],[40,52],[43,56],[46,59]], [[1,2],[4,5],[6,8],[9,11],[14,15],[17,18],[19,21],[22,24],[25,27],[28,30],[32,33],[35,36],[37,54],[38,53],[39,52],[40,51],[41,50],[42,49],[43,58],[44,60],[45,59],[46,55],[47,57],[48,56]], [[1,4],[2,7,6,11],[5,10,9,8],[15,20,19,21],[18,23,22,24],[25,49,61,37],[26,32,55,41],[27,54,47,34],[28,52,62,40],[29,35,58,38],[30,51,44,31],[33,59,64,46],[36,56,63,43],[39,60],[42,57],[45,50],[48,53]], [[0,1],[3,4],[7,8],[10,11],[13,14],[16,17],[20,21],[23,24],[26,27],[29,30],[31,32],[34,35],[37,52],[38,54],[39,53],[40,49],[41,51],[42,50],[43,59],[44,58],[45,60],[46,56],[47,55],[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 (1) b (1) c a (1) bc ac (1) bc abcc (1) c cc Design No 5(for Input Group of Order 12 and Index 1) Group Size 1536 C9039295 77FCE5FE Group generators (treatments are numbered (1) c cc b bc bcc a ac acc ab abc abcc ) Treatments are numbered first (invariants LAST therein), then blocks, then sub-blocks, if applicable, then replicates, if applicable [[20,23]], [[21,24]], [[19,22]], [[15,18]], [[14,17]], [[13,16]], [[1,2],[4,5],[6,8],[9,11],[14,15],[17,18],[19,21],[22,24],[25,27],[28,30],[32,33],[35,36],[37,54],[38,53],[39,52],[40,51],[41,50],[42,49],[43,58],[44,60],[45,59],[46,55],[47,57],[48,56]], [[0,1],[3,4],[7,8],[10,11],[13,14],[16,17],[20,21],[23,24],[26,27],[29,30],[31,32],[34,35],[37,52],[38,54],[39,53],[40,49],[41,51],[42,50],[43,59],[44,58],[45,60],[46,56],[47,55],[48,57]], [[0,3],[1,4],[2,5],[6,9],[7,10],[8,11],[25,28],[26,29],[27,30],[31,34],[32,35],[33,36],[37,40],[38,41],[39,42],[43,46],[44,47],[45,48],[49,52],[50,53],[51,54],[55,58],[56,59],[57,60],[61,62],[63,64]], [[0,6,4,10,2,8,3,9,1,7,5,11],[13,19,14,20,15,21],[16,22,17,23,18,24],[25,32,29,36,27,31,28,35,26,33,30,34],[37,59,41,57,39,58,40,56,38,60,42,55],[43,49,47,53,45,51,46,52,44,50,48,54],[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 (1) b (1) c a (1) bc acc (1) bc abc (1) c cc Design No 6(for Input Group of Order 12 and Index 1) Group Size 12 50D1F95E 2C70D1CE Block Intersection Formula {(0)^21 (1)^27 (2)^3 (3)^1 }^52 Initial Blocks, in the group representation, last block PC(4): 1000 (1) bc (1) c a (1) b ac (1) bc a (1) c cc