Design No 1(for Input Group of Order 16 and Index 11) Group Size 32 2E744276 71610FED 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],[52,53],[58,59]], [[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],[54,55],[56,57]], [[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)^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 c b a () d bc ac abc () c ad ab abcd Design No 2(for Input Group of Order 16 and Index 11) Group Size 16 AAC147DC A697810B 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 c b ab () d bc ac abcd () c bd a acd Design No 3(for Input Group of Order 16 and Index 11) Group Size 16 3FE7EEB8 53F497C5 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 c b ab () d bc ac abcd () c bd ad ac Design No 4(for Input Group of Order 16 and Index 11) Group Size 32 795A5D5A 5C6F82DF 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)^6 (1)^13 (2)^27 (3)^1 (5)^1 }^32 {(0)^7 (1)^10 (2)^30 (5)^1 }^16 Initial Blocks, in the group representation: () d b bc a () d ac ab abcd () c a acd ab Design No 5(for Input Group of Order 16 and Index 11) Group Size 32 1E842F1B BFDB8323 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 }^32 {(0)^7 (1)^10 (2)^30 (5)^1 }^16 Initial Blocks, in the group representation: () d b bc a () d ac ab abcd () c a acd abcd Design No 6(for Input Group of Order 16 and Index 11) Group Size 192 4B76706B 23238DCA 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],[8,10],[9,11],[12,13],[14,15],[16,17],[18,19],[20,22],[21,23],[24,27],[25,26],[32,33],[34,35],[36,38],[37,39],[40,43],[41,42],[48,50],[49,51],[52,53],[54,55],[60,63],[61,62]], [[2,3],[4,8,7,10],[5,9,6,11],[12,14,13,15],[16,32,17,33],[18,35,19,34],[20,40,22,43],[21,41,23,42],[24,39,27,37],[25,38,26,36],[28,46],[29,47],[30,45],[31,44],[48,63,50,60],[49,62,51,61],[52,54,53,55],[58,59]], [[1,2],[4,5,7,6],[8,13,10,12],[9,15,11,14],[16,20,17,22],[18,21,19,23],[24,26,27,25],[28,31],[32,48,33,50],[34,49,35,51],[36,53,38,52],[37,55,39,54],[40,63,43,60],[41,61,42,62],[44,58],[45,56],[46,59],[47,57]], [[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]], [[0,4],[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)^7 (1)^10 (2)^30 (5)^1 }^48 Initial Blocks, in the group representation: () d b bc ab () d a acd abc () c ad abd abc