Design No 1(for Input Group of Order 12 and Index 4) 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
[[46,58]],
[[48,60]],
[[47,59]],
[[41,53]],
[[43,55]],
[[39,51]],
[[38,50]],
[[45,57]],
[[40,52]],
[[37,49]],
[[42,54]],
[[44,56]],
[[3,6,9],[4,7,10],[5,8,11],[16,19,22],[17,20,23],[18,21,24],[25,31,28],[26,32,29],[27,33,30],[37,44,42],[38,45,40],[39,43,41],[46,47,48],[49,56,54],[50,57,52],[51,55,53],[58,59,60],[62,63,64]],
[[1,2],[4,5],[6,9],[7,11],[8,10],[13,15],[16,18],[19,24],[20,23],[21,22],[25,28],[26,30],[27,29],[32,33],[35,36],[37,42],[38,41],[39,40],[43,45],[46,48],[49,54],[50,53],[51,52],[55,57],[58,60],[63,64]],
[[0,1],[3,4],[6,10],[7,9],[8,11],[14,15],[17,18],[19,22],[20,24],[21,23],[25,29],[26,28],[27,30],[31,32],[34,35],[37,40],[38,42],[39,41],[44,45],[47,48],[49,52],[50,54],[51,53],[56,57],[59,60],[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 4) 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],[16,19],[17,20],[18,21],[28,31],[29,32],[30,33],[37,54],[38,52],[39,53],[40,60],[41,58],[42,59],[43,51],[44,49],[45,50],[46,57],[47,55],[48,56],[62,63]],
[[1,2],[4,5],[7,8],[10,11],[13,15],[16,18],[19,21],[22,24],[26,27],[29,30],[32,33],[35,36],[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],[3,4],[6,7],[9,10],[14,15],[17,18],[20,21],[23,24],[25,26],[28,29],[31,32],[34,35],[37,52],[38,54],[39,53],[40,49],[41,51],[42,50],[43,58],[44,60],[45,59],[46,55],[47,57],[48,56]],
[[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 4) Group Size 24 84034AF8 2F845DFE
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
[[3,6],[4,7],[5,8],[16,19],[17,20],[18,21],[25,37],[26,38],[27,39],[28,43],[29,44],[30,45],[31,40],[32,41],[33,42],[34,46],[35,47],[36,48],[52,55],[53,56],[54,57],[62,63]],
[[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],[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 }^52 
Initial Blocks, in the group representation, last block PC(4):
1000 (1) c 
(1) b ac 
(1) bc a 
(1) bc ac 
(1) c cc 

Design No 4(for Input Group of Order 12 and Index 4) Group Size 72 640D10C0 CC57FC28
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],[16,19],[17,20],[18,21],[25,37],[26,38],[27,39],[28,43],[29,44],[30,45],[31,40],[32,41],[33,42],[34,46],[35,47],[36,48],[49,58],[50,59],[51,60],[62,63]],
[[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],[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 ac 
(1) bc a 
(1) bc ab 
(1) c cc