Design No 1(for Input Group of Order 16 and Index 4) Group Size 16 6B6AF410 364C7E7B
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 abcd 
() c bd a abc 

Design No 2(for Input Group of Order 16 and Index 4) Group Size 16 7984321B 3BC1ACF6
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 a abc 

Design No 3(for Input Group of Order 16 and Index 4) Group Size 16 3AA19093 3E0807FA
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 c b a 
() d ac ab abcd 
() c bd a ab 

Design No 4(for Input Group of Order 16 and Index 4) 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
[[1,3],[5,7],[8,14],[9,13],[10,12],[11,15],[16,18],[20,22],[24,28],[25,31],[26,30],[27,29],[32,36],[33,39],[34,38],[35,37],[41,43],[45,47],[48,50],[52,54],[56,60],[57,63],[58,62],[59,61]],
[[1,5,3,7],[4,6],[8,13,14,9],[10,15,12,11],[16,48,18,50],[17,53],[19,55],[20,54,22,52],[21,51],[23,49],[24,63,28,57],[25,58,31,62],[26,61,30,59],[27,56,29,60],[32,33,36,39],[34,35,38,37],[41,45,43,47],[44,46]],
[[1,8,11],[2,6,4],[3,14,15],[5,10,13],[7,12,9],[16,25,32],[17,53,42],[18,31,36],[19,51,46],[20,27,38],[21,55,44],[22,29,34],[23,49,40],[24,45,59],[26,43,63],[28,47,61],[30,41,57],[33,58,48],[35,60,52],[37,56,54],[39,62,50]],
[[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]]
Block Intersection Formula 
{(0)^7 (1)^10 (2)^30 (5)^1 }^48 
Initial Blocks, in the group representation:
() d c a ab 
() d b bcd acd 
() c bd acd abd 

Design No 5(for Input Group of Order 16 and Index 4) Group Size 16 EFEE3096 5FCF4CE2
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 c a ab 
() d b bcd ab 
() c bd ad abcd 

Design No 6(for Input Group of Order 16 and Index 4) 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
[[1,3],[5,7],[8,14],[9,13],[10,12],[11,15],[16,18],[20,22],[24,28],[25,31],[26,30],[27,29],[32,36],[33,39],[34,38],[35,37],[41,43],[45,47],[48,50],[52,54],[56,60],[57,63],[58,62],[59,61]],
[[1,5,3,7],[4,6],[8,15,14,11],[9,10,13,12],[16,48,18,50],[17,53],[19,55],[20,54,22,52],[21,51],[23,49],[24,61,28,59],[25,56,31,60],[26,63,30,57],[27,58,29,62],[32,33,36,39],[34,35,38,37],[40,42],[41,47,43,45]],
[[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]],
[[0,8,1,9],[2,10,3,11],[4,14,5,15],[6,12,7,13],[16,24,17,25],[18,26,19,27],[20,30,21,31],[22,28,23,29],[32,40,33,41],[34,42,35,43],[36,46,37,47],[38,44,39,45],[48,56,49,57],[50,58,51,59],[52,62,53,63],[54,60,55,61]]
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 c a ab 
() d b bcd abd 
() c bd ad abcd 

Design No 7(for Input Group of Order 16 and Index 4) 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
[[1,3],[5,7],[8,14],[9,13],[10,12],[11,15],[16,18],[20,22],[24,28],[25,31],[26,30],[27,29],[32,36],[33,39],[34,38],[35,37],[41,43],[45,47],[48,50],[52,54],[56,60],[57,63],[58,62],[59,61]],
[[1,5,3,7],[4,6],[8,15,14,11],[9,10,13,12],[16,48,18,50],[17,53],[19,55],[20,54,22,52],[21,51],[23,49],[24,61,28,59],[25,56,31,60],[26,63,30,57],[27,58,29,62],[32,33,36,39],[34,35,38,37],[40,42],[41,47,43,45]],
[[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]],
[[0,8,1,9],[2,10,3,11],[4,14,5,15],[6,12,7,13],[16,24,17,25],[18,26,19,27],[20,30,21,31],[22,28,23,29],[32,40,33,41],[34,42,35,43],[36,46,37,47],[38,44,39,45],[48,56,49,57],[50,58,51,59],[52,62,53,63],[54,60,55,61]]
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 a ab 
() d b bcd abcd 
() c bd ad abcd 

Design No 8(for Input Group of Order 16 and Index 4) 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],[16,25],[17,24],[18,27],[19,26],[20,28],[21,29],[22,30],[23,31],[32,41],[33,40],[34,43],[35,42],[36,44],[37,45],[38,46],[39,47],[48,58],[49,59],[50,56],[51,57],[52,63],[53,62],[54,61],[55,60]]
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 9(for Input Group of Order 16 and Index 4) 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],[16,25],[17,24],[18,27],[19,26],[20,28],[21,29],[22,30],[23,31],[32,41],[33,40],[34,43],[35,42],[36,44],[37,45],[38,46],[39,47],[48,58],[49,59],[50,56],[51,57],[52,63],[53,62],[54,61],[55,60]]
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 10(for Input Group of Order 16 and Index 4) 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],[8,10],[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]],
[[0,1],[2,3],[4,6],[5,7],[8,11],[9,10],[20,23],[21,22],[24,26],[25,27],[28,29],[30,31],[36,39],[37,38],[40,42],[41,43],[44,45],[46,47],[48,51],[49,50],[56,57],[58,59],[60,62],[61,63]],
[[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]],
[[0,8,3,11],[1,9,2,10],[4,13,7,14],[5,12,6,15],[16,25,19,26],[17,24,18,27],[20,28,23,31],[21,29,22,30],[32,41,35,42],[33,40,34,43],[36,44,39,47],[37,45,38,46],[48,58,51,57],[49,59,50,56],[52,63,55,60],[53,62,54,61]]
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 b bc ab 
() d a acd ab 
() c ad ab abcd 

Design No 11(for Input Group of Order 16 and Index 4) Group Size 960 6149AA3D 610F8BC9
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
[[4,6],[5,7],[8,9],[10,11],[12,15],[13,14],[16,17],[18,19],[20,23],[21,22],[28,30],[29,31],[32,33],[34,35],[36,39],[37,38],[44,46],[45,47],[48,50],[49,51],[56,59],[57,58],[60,61],[62,63]],
[[2,3],[4,12,6,15],[5,13,7,14],[8,10,9,11],[16,32,17,33],[18,35,19,34],[20,45,23,47],[21,44,22,46],[24,42],[25,43],[26,41],[27,40],[28,39,30,36],[29,38,31,37],[48,58,50,57],[49,59,51,56],[54,55],[60,63,61,62]],
[[1,2,3],[4,14,9,6,13,8],[5,12,10,7,15,11],[16,47,57,17,45,58],[18,44,56,19,46,59],[20,32,50,23,33,48],[21,34,49,22,35,51],[24,41,54],[25,43,53],[26,42,55],[27,40,52],[28,38,61,30,37,60],[29,36,62,31,39,63]],
[[1,4],[2,13],[3,9],[6,12],[7,8],[11,14],[17,20],[18,28],[19,24],[22,29],[23,25],[26,31],[32,43],[33,47],[34,39],[36,42],[37,46],[41,44],[48,53],[50,58],[51,62],[54,59],[55,63],[56,61]],
[[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]]
Block Intersection Formula 
{(0)^7 (1)^10 (2)^30 (5)^1 }^48 
Initial Blocks, in the group representation:
() d b bcd a 
() d ac ab abc 
() c bd a acd 

Design No 12(for Input Group of Order 16 and Index 4) Group Size 64 6AEF1790 00DCEFD7
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
[[4,6],[5,7],[8,11],[9,10],[12,13],[14,15],[16,17],[18,19],[20,23],[21,22],[24,26],[25,27],[32,33],[34,35],[36,39],[37,38],[40,42],[41,43],[48,50],[49,51],[56,57],[58,59],[60,63],[61,62]],
[[1,3],[4,5,6,7],[8,13,11,12],[9,14,10,15],[16,20,17,23],[18,22,19,21],[24,27,26,25],[28,30],[32,63,33,60],[34,61,35,62],[36,58,39,59],[37,57,38,56],[40,49,42,51],[41,50,43,48],[44,52],[45,55],[46,54],[47,53]],
[[0,1],[2,3],[4,7],[5,6],[8,10],[9,11],[20,22],[21,23],[24,27],[25,26],[28,29],[30,31],[36,38],[37,39],[40,43],[41,42],[44,45],[46,47],[48,51],[49,50],[52,53],[54,55],[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],[4,14,5,15],[6,12,7,13],[16,24,17,25],[18,26,19,27],[20,30,21,31],[22,28,23,29],[32,40,33,41],[34,42,35,43],[36,46,37,47],[38,44,39,45],[48,56,49,57],[50,58,51,59],[52,62,53,63],[54,60,55,61]]
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 b bcd ab 
() d a ac ab 
() c bd ab abcd 

Design No 13(for Input Group of Order 16 and Index 4) Group Size 32 5614F577 F31C4E74
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
[[4,6],[5,7],[8,11],[9,10],[12,13],[14,15],[16,17],[18,19],[20,23],[21,22],[24,26],[25,27],[32,33],[34,35],[36,39],[37,38],[40,42],[41,43],[48,50],[49,51],[56,57],[58,59],[60,63],[61,62]],
[[0,1],[2,3],[4,7],[5,6],[8,10],[9,11],[20,22],[21,23],[24,27],[25,26],[28,29],[30,31],[36,38],[37,39],[40,43],[41,42],[44,45],[46,47],[48,51],[49,50],[52,53],[54,55],[60,62],[61,63]],
[[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]],
[[0,8,2,10],[1,9,3,11],[4,12,6,14],[5,13,7,15],[16,25,18,27],[17,24,19,26],[20,29,22,31],[21,28,23,30],[32,41,34,43],[33,40,35,42],[36,45,38,47],[37,44,39,46],[48,58,50,56],[49,59,51,57],[52,62,54,60],[53,63,55,61]]
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 b bcd ab 
() d a ac ab 
() c bd abd abc 

Design No 14(for Input Group of Order 16 and Index 4) Group Size 64 061BA30D 8A7FB4F0
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
[[4,6],[5,7],[8,11],[9,10],[12,13],[14,15],[16,17],[18,19],[20,23],[21,22],[24,26],[25,27],[32,33],[34,35],[36,39],[37,38],[40,42],[41,43],[48,50],[49,51],[56,57],[58,59],[60,63],[61,62]],
[[1,3],[4,5,6,7],[8,13,11,12],[9,14,10,15],[16,20,17,23],[18,22,19,21],[24,27,26,25],[28,30],[32,61,33,62],[34,63,35,60],[36,56,39,57],[37,59,38,58],[40,51,42,49],[41,48,43,50],[44,54],[45,53],[46,52],[47,55]],
[[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]],
[[0,8,1,9],[2,10,3,11],[4,14,5,15],[6,12,7,13],[16,24,17,25],[18,26,19,27],[20,30,21,31],[22,28,23,29],[32,40,33,41],[34,42,35,43],[36,46,37,47],[38,44,39,45],[48,56,49,57],[50,58,51,59],[52,62,53,63],[54,60,55,61]]
Block Intersection Formula 
{(0)^3 (1)^22 (2)^18 (3)^4 (5)^1 }^16 
{(0)^5 (1)^16 (2)^24 (3)^2 (5)^1 }^32 
Initial Blocks, in the group representation:
() d b bcd ab 
() d a ac abc 
() c bd abd abc