Design No 1(for Input Group of Order 16 and Index 4) Group Size 0 C05C7B74 60C429F9
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^16 
{(0)^39 (1)^39 (3)^2 }^64 
Initial Blocks, in the group representation:
() d c 
() b a 
() b a 
() bd ac 
() bd ac 

Design No 2(for Input Group of Order 16 and Index 4) Group Size 2097152 4A35AA3B 5CF5A92F
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
[[47,63]],
[[46,62]],
[[44,60]],
[[45,61]],
[[35,51]],
[[42,58]],
[[37,53]],
[[43,59]],
[[34,50]],
[[36,52]],
[[39,55]],
[[40,56]],
[[33,49]],
[[41,57]],
[[38,54]],
[[32,48]],
[[4,6],[5,7],[8,14],[9,15],[10,12],[11,13],[20,22],[21,23],[24,30],[25,31],[26,28],[27,29],[32,38],[33,39],[34,36],[35,37],[44,46],[45,47],[48,54],[49,55],[50,52],[51,53],[60,62],[61,63],[64,87],[65,86],[66,85],[67,84],[68,83],[69,82],[70,81],[71,80],[72,89],[73,88],[74,91],[75,90],[76,95],[77,94],[78,93],[79,92]],
[[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],[64,65],[66,67],[68,69],[70,71],[72,73],[74,75],[76,77],[78,79],[80,81],[82,83],[84,85],[86,87],[88,89],[90,91],[92,93],[94,95]],
[[0,2],[1,3],[8,12],[9,13],[10,14],[11,15],[16,18],[17,19],[24,28],[25,29],[26,30],[27,31],[32,36],[33,37],[34,38],[35,39],[40,42],[41,43],[48,52],[49,53],[50,54],[51,55],[56,58],[57,59],[64,85],[65,84],[66,87],[67,86],[68,81],[69,80],[70,83],[71,82],[72,91],[73,90],[74,89],[75,88],[76,93],[77,92],[78,95],[79,94]],
[[0,4],[1,5],[2,6],[3,7],[12,14],[13,15],[16,20],[17,21],[18,22],[19,23],[28,30],[29,31],[36,38],[37,39],[40,44],[41,45],[42,46],[43,47],[52,54],[53,55],[56,60],[57,61],[58,62],[59,63],[64,81],[65,80],[66,83],[67,82],[68,87],[69,86],[70,85],[71,84],[72,93],[73,92],[74,95],[75,94],[76,89],[77,88],[78,91],[79,90]],
[[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],[64,72,65,73],[66,74,67,75],[68,78,69,79],[70,76,71,77],[80,88,81,89],[82,90,83,91],[84,94,85,95],[86,92,87,93]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^48 
{(0)^39 (1)^39 (3)^2 }^32 
Initial Blocks, in the group representation:
() d c 
() b a 
() b a 
() bd ac 
() bd acd 

Design No 3(for Input Group of Order 16 and Index 4) Group Size 128 EE43FC02 DD893234
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
[[8,9],[10,11],[12,13],[14,15],[24,25],[26,27],[28,29],[30,31],[32,48],[33,49],[34,50],[35,51],[36,52],[37,53],[38,54],[39,55],[40,57],[41,56],[42,59],[43,58],[44,61],[45,60],[46,63],[47,62],[64,80],[65,81],[66,82],[67,83],[68,84],[69,85],[70,86],[71,87],[72,89],[73,88],[74,91],[75,90],[76,93],[77,92],[78,95],[79,94]],
[[4,5],[6,7],[8,10],[9,11],[12,15],[13,14],[20,21],[22,23],[24,26],[25,27],[28,31],[29,30],[32,64],[33,65],[34,66],[35,67],[36,69],[37,68],[38,71],[39,70],[40,74],[41,75],[42,72],[43,73],[44,79],[45,78],[46,77],[47,76],[48,80],[49,81],[50,82],[51,83],[52,85],[53,84],[54,87],[55,86],[56,90],[57,91],[58,88],[59,89],[60,95],[61,94],[62,93],[63,92]],
[[4,6],[5,7],[8,14],[9,15],[10,12],[11,13],[20,22],[21,23],[24,30],[25,31],[26,28],[27,29],[32,38],[33,39],[34,36],[35,37],[44,46],[45,47],[48,54],[49,55],[50,52],[51,53],[60,62],[61,63],[64,87],[65,86],[66,85],[67,84],[68,83],[69,82],[70,81],[71,80],[72,89],[73,88],[74,91],[75,90],[76,95],[77,94],[78,93],[79,92]],
[[0,1],[2,3],[8,10],[9,11],[12,15],[13,14],[16,17],[18,19],[24,26],[25,27],[28,31],[29,30],[32,81],[33,80],[34,83],[35,82],[36,84],[37,85],[38,86],[39,87],[40,90],[41,91],[42,88],[43,89],[44,95],[45,94],[46,93],[47,92],[48,65],[49,64],[50,67],[51,66],[52,68],[53,69],[54,70],[55,71],[56,74],[57,75],[58,72],[59,73],[60,79],[61,78],[62,77],[63,76]],
[[0,2],[1,3],[8,12],[9,13],[10,14],[11,15],[16,18],[17,19],[24,28],[25,29],[26,30],[27,31],[32,36],[33,37],[34,38],[35,39],[40,42],[41,43],[48,52],[49,53],[50,54],[51,55],[56,58],[57,59],[64,85],[65,84],[66,87],[67,86],[68,81],[69,80],[70,83],[71,82],[72,91],[73,90],[74,89],[75,88],[76,93],[77,92],[78,95],[79,94]],
[[0,4],[1,5],[2,6],[3,7],[12,14],[13,15],[16,20],[17,21],[18,22],[19,23],[28,30],[29,31],[36,38],[37,39],[40,44],[41,45],[42,46],[43,47],[52,54],[53,55],[56,60],[57,61],[58,62],[59,63],[64,81],[65,80],[66,83],[67,82],[68,87],[69,86],[70,85],[71,84],[72,93],[73,92],[74,95],[75,94],[76,89],[77,88],[78,91],[79,90]],
[[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],[32,56],[33,57],[34,58],[35,59],[36,62],[37,63],[38,60],[39,61],[40,48],[41,49],[42,50],[43,51],[44,54],[45,55],[46,52],[47,53],[64,88],[65,89],[66,90],[67,91],[68,94],[69,95],[70,92],[71,93],[72,80],[73,81],[74,82],[75,83],[76,86],[77,87],[78,84],[79,85]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d c 
() b a 
() b ad 
() bd ac 
() bd acd 

Design No 4(for Input Group of Order 16 and Index 4) Group Size 128 E7D9560D 999EC67C
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
[[8,10],[9,11],[12,14],[13,15],[24,26],[25,27],[28,30],[29,31],[32,48],[33,49],[34,50],[35,51],[36,52],[37,53],[38,54],[39,55],[40,58],[41,59],[42,56],[43,57],[44,62],[45,63],[46,60],[47,61],[64,80],[65,81],[66,82],[67,83],[68,84],[69,85],[70,86],[71,87],[72,90],[73,91],[74,88],[75,89],[76,94],[77,95],[78,92],[79,93]],
[[4,5],[6,7],[12,13],[14,15],[20,21],[22,23],[28,29],[30,31],[32,64],[33,65],[34,66],[35,67],[36,69],[37,68],[38,71],[39,70],[40,72],[41,73],[42,74],[43,75],[44,77],[45,76],[46,79],[47,78],[48,80],[49,81],[50,82],[51,83],[52,85],[53,84],[54,87],[55,86],[56,88],[57,89],[58,90],[59,91],[60,93],[61,92],[62,95],[63,94]],
[[1,2],[4,8],[5,10],[6,9],[7,11],[12,15],[17,18],[20,24],[21,26],[22,25],[23,27],[28,31],[33,34],[36,72],[37,74],[38,73],[39,75],[40,52],[41,54],[42,53],[43,55],[44,95],[45,93],[46,94],[47,92],[48,64],[49,66],[50,65],[51,67],[56,84],[57,86],[58,85],[59,87],[60,63],[68,88],[69,90],[70,89],[71,91],[76,79],[81,82]],
[[0,1],[2,3],[8,9],[10,11],[16,17],[18,19],[24,25],[26,27],[32,65],[33,64],[34,67],[35,66],[36,68],[37,69],[38,70],[39,71],[40,73],[41,72],[42,75],[43,74],[44,76],[45,77],[46,78],[47,79],[48,81],[49,80],[50,83],[51,82],[52,84],[53,85],[54,86],[55,87],[56,89],[57,88],[58,91],[59,90],[60,92],[61,93],[62,94],[63,95]],
[[0,4,2,6],[1,5,3,7],[8,12,10,14],[9,13,11,15],[16,20,18,22],[17,21,19,23],[24,28,26,30],[25,29,27,31],[32,36,34,38],[33,37,35,39],[40,44,42,46],[41,45,43,47],[48,52,50,54],[49,53,51,55],[56,60,58,62],[57,61,59,63],[64,68,66,70],[65,69,67,71],[72,76,74,78],[73,77,75,79],[80,84,82,86],[81,85,83,87],[88,92,90,94],[89,93,91,95]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d c 
() b a 
() b ac 
() bd a 
() bd ac 

Design No 5(for Input Group of Order 16 and Index 4) Group Size 32 834C5410 C121B97F
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],[8,12],[9,13],[10,14],[11,15],[20,22],[21,23],[24,28],[25,29],[26,30],[27,31],[32,54],[33,55],[34,52],[35,53],[36,50],[37,51],[38,48],[39,49],[40,58],[41,59],[42,56],[43,57],[44,60],[45,61],[46,62],[47,63],[64,87],[65,86],[66,85],[67,84],[68,83],[69,82],[70,81],[71,80],[72,91],[73,90],[74,89],[75,88],[76,93],[77,92],[78,95],[79,94]],
[[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],[64,65],[66,67],[68,69],[70,71],[72,73],[74,75],[76,77],[78,79],[80,81],[82,83],[84,85],[86,87],[88,89],[90,91],[92,93],[94,95]],
[[0,2],[1,3],[8,14],[9,15],[10,12],[11,13],[16,18],[17,19],[24,30],[25,31],[26,28],[27,29],[32,52],[33,53],[34,54],[35,55],[36,48],[37,49],[38,50],[39,51],[40,56],[41,57],[42,58],[43,59],[44,62],[45,63],[46,60],[47,61],[64,85],[65,84],[66,87],[67,86],[68,81],[69,80],[70,83],[71,82],[72,89],[73,88],[74,91],[75,90],[76,95],[77,94],[78,93],[79,92]],
[[0,4],[1,5],[2,6],[3,7],[8,10],[9,11],[16,20],[17,21],[18,22],[19,23],[24,26],[25,27],[32,48],[33,49],[34,50],[35,51],[36,54],[37,55],[38,52],[39,53],[40,62],[41,63],[42,60],[43,61],[44,58],[45,59],[46,56],[47,57],[64,81],[65,80],[66,83],[67,82],[68,87],[69,86],[70,85],[71,84],[72,95],[73,94],[74,93],[75,92],[76,91],[77,90],[78,89],[79,88]],
[[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],[64,72,65,73],[66,74,67,75],[68,78,69,79],[70,76,71,77],[80,88,81,89],[82,90,83,91],[84,94,85,95],[86,92,87,93]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d c 
() b a 
() b ac 
() bd a 
() bd acd 

Design No 6(for Input Group of Order 16 and Index 4) Group Size 32 52575E4D 922F4C00
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],[8,14],[9,15],[10,12],[11,13],[20,22],[21,23],[24,30],[25,31],[26,28],[27,29],[32,38],[33,39],[34,36],[35,37],[44,46],[45,47],[48,54],[49,55],[50,52],[51,53],[60,62],[61,63],[64,87],[65,86],[66,85],[67,84],[68,83],[69,82],[70,81],[71,80],[72,89],[73,88],[74,91],[75,90],[76,95],[77,94],[78,93],[79,92]],
[[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],[64,65],[66,67],[68,69],[70,71],[72,73],[74,75],[76,77],[78,79],[80,81],[82,83],[84,85],[86,87],[88,89],[90,91],[92,93],[94,95]],
[[0,2],[1,3],[8,12],[9,13],[10,14],[11,15],[16,18],[17,19],[24,28],[25,29],[26,30],[27,31],[32,36],[33,37],[34,38],[35,39],[40,42],[41,43],[48,52],[49,53],[50,54],[51,55],[56,58],[57,59],[64,85],[65,84],[66,87],[67,86],[68,81],[69,80],[70,83],[71,82],[72,91],[73,90],[74,89],[75,88],[76,93],[77,92],[78,95],[79,94]],
[[0,4],[1,5],[2,6],[3,7],[12,14],[13,15],[16,20],[17,21],[18,22],[19,23],[28,30],[29,31],[36,38],[37,39],[40,44],[41,45],[42,46],[43,47],[52,54],[53,55],[56,60],[57,61],[58,62],[59,63],[64,81],[65,80],[66,83],[67,82],[68,87],[69,86],[70,85],[71,84],[72,93],[73,92],[74,95],[75,94],[76,89],[77,88],[78,91],[79,90]],
[[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],[64,72,65,73],[66,74,67,75],[68,78,69,79],[70,76,71,77],[80,88,81,89],[82,90,83,91],[84,94,85,95],[86,92,87,93]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d c 
() b a 
() b ac 
() bd ab 
() bd abcd 

Design No 7(for Input Group of Order 16 and Index 4) Group Size 12288 48CF51D6 B78CEA52
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
[[5,6],[21,22],[33,70],[34,69],[37,83],[38,80],[44,60],[47,63],[49,86],[50,85],[53,67],[54,64],[72,88],[75,91]],
[[13,14],[29,30],[37,53],[38,54],[40,77],[43,78],[45,89],[46,90],[56,93],[59,94],[61,73],[62,74],[64,80],[67,83]],
[[9,10],[25,26],[33,49],[34,50],[41,95],[42,92],[45,74],[46,73],[57,79],[58,76],[61,90],[62,89],[69,85],[70,86]],
[[12,15],[28,31],[36,52],[39,55],[41,76],[42,79],[44,88],[47,91],[57,92],[58,95],[60,72],[63,75],[65,81],[66,82]],
[[8,11],[24,27],[32,48],[35,51],[40,94],[43,93],[44,75],[47,72],[56,78],[59,77],[60,91],[63,88],[68,84],[71,87]],
[[4,5],[6,7],[8,13],[9,12],[10,15],[11,14],[20,21],[22,23],[24,29],[25,28],[26,31],[27,30],[32,64],[33,65],[34,66],[35,67],[36,85],[37,84],[38,87],[39,86],[40,59],[41,58],[42,57],[43,56],[44,45],[46,47],[48,80],[49,81],[50,82],[51,83],[52,69],[53,68],[54,71],[55,70],[60,61],[62,63],[72,90],[73,91],[74,88],[75,89]],
[[4,8],[5,9],[6,10],[7,11],[12,13],[14,15],[20,24],[21,25],[22,26],[23,27],[28,29],[30,31],[36,93],[37,92],[38,95],[39,94],[40,81],[41,80],[42,83],[43,82],[44,45],[46,47],[48,71],[49,70],[50,69],[51,68],[52,56],[53,57],[54,58],[55,59],[60,74],[61,75],[62,72],[63,73],[64,76],[65,77],[66,78],[67,79],[88,89],[90,91]],
[[1,2],[17,18],[33,85],[34,86],[36,65],[39,66],[40,56],[43,59],[49,69],[50,70],[52,81],[55,82],[77,93],[78,94]],
[[0,1],[2,3],[8,12],[9,13],[10,14],[11,15],[16,17],[18,19],[24,28],[25,29],[26,30],[27,31],[32,65],[33,64],[34,67],[35,66],[36,84],[37,85],[38,86],[39,87],[40,58],[41,59],[42,56],[43,57],[48,81],[49,80],[50,83],[51,82],[52,68],[53,69],[54,70],[55,71],[72,91],[73,90],[74,89],[75,88],[76,77],[78,79],[92,93],[94,95]],
[[0,4],[1,5],[2,6],[3,7],[12,13],[14,15],[16,20],[17,21],[18,22],[19,23],[28,29],[30,31],[36,54],[37,55],[38,52],[39,53],[40,88],[41,89],[42,90],[43,91],[44,77],[45,76],[46,79],[47,78],[56,72],[57,73],[58,74],[59,75],[60,93],[61,92],[62,95],[63,94],[64,65],[66,67],[68,87],[69,86],[70,85],[71,84],[80,81],[82,83]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d c 
() b a 
() b acd 
() bd abd 
() bd abc 

Design No 8(for Input Group of Order 16 and Index 4) Group Size 16 2E195131 D6ADAF8A
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d c 
() b a 
() b ab 
() bd ac 
() bd abc 

Design No 9(for Input Group of Order 16 and Index 4) Group Size 384 A88C3351 DCBE35FC
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
[[4,5],[6,7],[8,11],[9,10],[12,14],[13,15],[20,21],[22,23],[24,27],[25,26],[28,30],[29,31],[32,64],[33,65],[34,66],[35,67],[36,69],[37,68],[38,71],[39,70],[40,75],[41,74],[42,73],[43,72],[44,78],[45,79],[46,76],[47,77],[48,80],[49,81],[50,82],[51,83],[52,85],[53,84],[54,87],[55,86],[56,91],[57,90],[58,89],[59,88],[60,94],[61,95],[62,92],[63,93]],
[[4,6],[5,7],[8,9],[10,11],[12,15],[13,14],[20,22],[21,23],[24,25],[26,27],[28,31],[29,30],[32,54],[33,55],[34,52],[35,53],[36,50],[37,51],[38,48],[39,49],[40,61],[41,60],[42,63],[43,62],[44,57],[45,56],[46,59],[47,58],[64,87],[65,86],[66,85],[67,84],[68,83],[69,82],[70,81],[71,80],[72,92],[73,93],[74,94],[75,95],[76,88],[77,89],[78,90],[79,91]],
[[2,3],[4,8],[5,9],[6,11],[7,10],[12,13],[16,17],[20,25],[21,24],[22,26],[23,27],[30,31],[34,35],[36,93],[37,92],[38,94],[39,95],[40,81],[41,80],[42,82],[43,83],[44,45],[48,60],[49,61],[50,63],[51,62],[52,67],[53,66],[54,64],[55,65],[56,78],[57,79],[58,77],[59,76],[68,72],[69,73],[70,75],[71,74],[84,85],[90,91]],
[[1,2],[5,6],[8,13],[9,15],[10,12],[11,14],[17,18],[21,22],[24,29],[25,31],[26,28],[27,30],[32,48],[33,50],[34,49],[35,51],[36,65],[37,67],[38,64],[39,66],[40,43],[44,90],[45,88],[46,91],[47,89],[52,81],[53,83],[54,80],[55,82],[56,59],[60,74],[61,72],[62,75],[63,73],[68,84],[69,86],[70,85],[71,87],[76,79],[92,95]],
[[0,1],[4,8,7,10],[5,9,6,11],[12,15,13,14],[18,19],[20,25,23,27],[21,24,22,26],[28,30,29,31],[32,55,87,65],[33,54,86,64],[34,52,85,66],[35,53,84,67],[36,72,82,62],[37,73,83,63],[38,75,80,61],[39,74,81,60],[40,71,95,48],[41,70,94,49],[42,68,93,51],[43,69,92,50],[44,57,90,78],[45,56,91,79],[46,58,88,77],[47,59,89,76]],
[[0,4],[1,6],[2,5],[3,7],[9,10],[12,15],[16,20],[17,22],[18,21],[19,23],[25,26],[28,31],[33,34],[36,80],[37,82],[38,81],[39,83],[40,56],[41,58],[42,57],[43,59],[44,72],[45,74],[46,73],[47,75],[49,50],[52,64],[53,66],[54,65],[55,67],[60,88],[61,90],[62,89],[63,91],[68,71],[76,95],[77,93],[78,94],[79,92],[84,87]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d c 
() b a 
() b abd 
() bd acd 
() bd abcd 

Design No 10(for Input Group of Order 16 and Index 4) Group Size 32 25335C90 1C7C8A13
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
[[4,5],[6,7],[8,10],[9,11],[12,15],[13,14],[16,17],[18,19],[24,27],[25,26],[28,30],[29,31],[32,34],[33,35],[36,39],[37,38],[44,45],[46,47],[48,51],[49,50],[52,54],[53,55],[56,57],[58,59],[64,80],[65,81],[66,82],[67,83],[68,85],[69,84],[70,87],[71,86],[72,90],[73,91],[74,88],[75,89],[76,95],[77,94],[78,93],[79,92]],
[[0,1],[2,3],[8,11],[9,10],[12,14],[13,15],[20,21],[22,23],[24,26],[25,27],[28,31],[29,30],[32,35],[33,34],[36,38],[37,39],[40,41],[42,43],[48,50],[49,51],[52,55],[53,54],[60,61],[62,63],[64,81],[65,80],[66,83],[67,82],[68,84],[69,85],[70,86],[71,87],[72,91],[73,90],[74,89],[75,88],[76,94],[77,95],[78,92],[79,93]],
[[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],[64,66],[65,67],[68,70],[69,71],[72,74],[73,75],[76,78],[77,79],[80,82],[81,83],[84,86],[85,87],[88,90],[89,91],[92,94],[93,95]],
[[0,4,2,6],[1,5,3,7],[8,12,10,14],[9,13,11,15],[16,20,18,22],[17,21,19,23],[24,28,26,30],[25,29,27,31],[32,36,34,38],[33,37,35,39],[40,44,42,46],[41,45,43,47],[48,52,50,54],[49,53,51,55],[56,60,58,62],[57,61,59,63],[64,68,66,70],[65,69,67,71],[72,76,74,78],[73,77,75,79],[80,84,82,86],[81,85,83,87],[88,92,90,94],[89,93,91,95]],
[[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],[64,72,65,73],[66,74,67,75],[68,78,69,79],[70,76,71,77],[80,88,81,89],[82,90,83,91],[84,94,85,95],[86,92,87,93]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d b 
() c a 
() cd ab 
() b a 
() bd ac 

Design No 11(for Input Group of Order 16 and Index 4) Group Size 16 384F8DFD 984BED02
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d b 
() c a 
() cd ab 
() b a 
() bd acd 

Design No 12(for Input Group of Order 16 and Index 4) Group Size 96 0E28C847 6AF1635E
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
[[4,5],[6,7],[8,10],[9,11],[12,15],[13,14],[16,17],[18,19],[24,27],[25,26],[28,30],[29,31],[32,34],[33,35],[36,39],[37,38],[44,45],[46,47],[48,51],[49,50],[52,54],[53,55],[56,57],[58,59],[64,80],[65,81],[66,82],[67,83],[68,85],[69,84],[70,87],[71,86],[72,90],[73,91],[74,88],[75,89],[76,95],[77,94],[78,93],[79,92]],
[[1,2,3],[4,8,12],[5,10,15],[6,11,13],[7,9,14],[16,32,48],[17,34,51],[18,35,49],[19,33,50],[20,42,60],[21,40,63],[22,41,61],[23,43,62],[24,46,55],[25,44,52],[26,45,54],[27,47,53],[28,36,59],[29,38,56],[30,39,58],[31,37,57],[64,72,87],[65,74,84],[66,75,86],[67,73,85],[68,83,91],[69,81,88],[70,80,90],[71,82,89],[77,78,79],[92,94,93]],
[[0,1],[2,3],[8,11],[9,10],[12,14],[13,15],[20,21],[22,23],[24,26],[25,27],[28,31],[29,30],[32,35],[33,34],[36,38],[37,39],[40,41],[42,43],[48,50],[49,51],[52,55],[53,54],[60,61],[62,63],[64,81],[65,80],[66,83],[67,82],[68,84],[69,85],[70,86],[71,87],[72,91],[73,90],[74,89],[75,88],[76,94],[77,95],[78,92],[79,93]],
[[0,4,2,6],[1,5,3,7],[8,12,10,14],[9,13,11,15],[16,20,18,22],[17,21,19,23],[24,28,26,30],[25,29,27,31],[32,36,34,38],[33,37,35,39],[40,44,42,46],[41,45,43,47],[48,52,50,54],[49,53,51,55],[56,60,58,62],[57,61,59,63],[64,68,66,70],[65,69,67,71],[72,76,74,78],[73,77,75,79],[80,84,82,86],[81,85,83,87],[88,92,90,94],[89,93,91,95]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d b 
() c a 
() cd ab 
() b ad 
() bd acd 

Design No 13(for Input Group of Order 16 and Index 4) Group Size 32 E46BF15F B7BF6028
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
[[4,5],[6,7],[8,10],[9,11],[12,15],[13,14],[16,17],[18,19],[24,27],[25,26],[28,30],[29,31],[32,34],[33,35],[36,39],[37,38],[44,45],[46,47],[48,51],[49,50],[52,54],[53,55],[56,57],[58,59],[64,80],[65,81],[66,82],[67,83],[68,85],[69,84],[70,87],[71,86],[72,90],[73,91],[74,88],[75,89],[76,95],[77,94],[78,93],[79,92]],
[[0,1],[2,3],[8,11],[9,10],[12,14],[13,15],[20,21],[22,23],[24,26],[25,27],[28,31],[29,30],[32,35],[33,34],[36,38],[37,39],[40,41],[42,43],[48,50],[49,51],[52,55],[53,54],[60,61],[62,63],[64,81],[65,80],[66,83],[67,82],[68,84],[69,85],[70,86],[71,87],[72,91],[73,90],[74,89],[75,88],[76,94],[77,95],[78,92],[79,93]],
[[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],[64,66],[65,67],[68,70],[69,71],[72,74],[73,75],[76,78],[77,79],[80,82],[81,83],[84,86],[85,87],[88,90],[89,91],[92,94],[93,95]],
[[0,4,2,6],[1,5,3,7],[8,12,10,14],[9,13,11,15],[16,20,18,22],[17,21,19,23],[24,28,26,30],[25,29,27,31],[32,36,34,38],[33,37,35,39],[40,44,42,46],[41,45,43,47],[48,52,50,54],[49,53,51,55],[56,60,58,62],[57,61,59,63],[64,68,66,70],[65,69,67,71],[72,76,74,78],[73,77,75,79],[80,84,82,86],[81,85,83,87],[88,92,90,94],[89,93,91,95]],
[[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],[64,72,65,73],[66,74,67,75],[68,78,69,79],[70,76,71,77],[80,88,81,89],[82,90,83,91],[84,94,85,95],[86,92,87,93]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d b 
() c a 
() cd ab 
() b ac 
() bd a 

Design No 14(for Input Group of Order 16 and Index 4) Group Size 16 C91B551D 3DC425F9
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d b 
() c a 
() cd ab 
() b ac 
() bd ad 

Design No 15(for Input Group of Order 16 and Index 4) Group Size 16 8F7D54D2 6DD0857C
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d b 
() c a 
() cd ab 
() b ab 
() bd abc 

Design No 16(for Input Group of Order 16 and Index 4) Group Size 16 5473DC3C 048FA6B4
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d b 
() c a 
() cd ab 
() b abc 
() bd ab 

Design No 17(for Input Group of Order 16 and Index 4) Group Size 96 CFF456D3 486D8262
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
[[4,5],[6,7],[8,10],[9,11],[12,15],[13,14],[16,17],[18,19],[24,27],[25,26],[28,30],[29,31],[32,34],[33,35],[36,39],[37,38],[44,45],[46,47],[48,51],[49,50],[52,54],[53,55],[56,57],[58,59],[64,80],[65,81],[66,82],[67,83],[68,85],[69,84],[70,87],[71,86],[72,90],[73,91],[74,88],[75,89],[76,95],[77,94],[78,93],[79,92]],
[[1,2,3],[4,8,12],[5,10,15],[6,11,13],[7,9,14],[16,32,48],[17,34,51],[18,35,49],[19,33,50],[20,42,60],[21,40,63],[22,41,61],[23,43,62],[24,46,55],[25,44,52],[26,45,54],[27,47,53],[28,36,59],[29,38,56],[30,39,58],[31,37,57],[64,87,92],[65,85,95],[66,84,93],[67,86,94],[68,76,81],[69,78,82],[70,79,80],[71,77,83],[72,74,73],[88,91,90]],
[[0,1],[2,3],[8,11],[9,10],[12,14],[13,15],[20,21],[22,23],[24,26],[25,27],[28,31],[29,30],[32,35],[33,34],[36,38],[37,39],[40,41],[42,43],[48,50],[49,51],[52,55],[53,54],[60,61],[62,63],[64,81],[65,80],[66,83],[67,82],[68,84],[69,85],[70,86],[71,87],[72,91],[73,90],[74,89],[75,88],[76,94],[77,95],[78,92],[79,93]],
[[0,4,2,6],[1,5,3,7],[8,12,10,14],[9,13,11,15],[16,20,18,22],[17,21,19,23],[24,28,26,30],[25,29,27,31],[32,36,34,38],[33,37,35,39],[40,44,42,46],[41,45,43,47],[48,52,50,54],[49,53,51,55],[56,60,58,62],[57,61,59,63],[64,68,66,70],[65,69,67,71],[72,76,74,78],[73,77,75,79],[80,84,82,86],[81,85,83,87],[88,92,90,94],[89,93,91,95]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d b 
() c a 
() cd ab 
() b abc 
() bd abd 

Design No 18(for Input Group of Order 16 and Index 4) Group Size 32 7BBA861F 8C7805B4
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],[32,34],[33,35],[40,43],[41,42],[44,45],[46,47],[48,51],[49,50],[52,53],[54,55],[56,58],[57,59],[64,87],[65,86],[66,85],[67,84],[68,83],[69,82],[70,81],[71,80],[72,92],[73,93],[74,94],[75,95],[76,88],[77,89],[78,90],[79,91]],
[[0,1],[2,3],[4,7],[5,6],[12,14],[13,15],[20,22],[21,23],[24,25],[26,27],[28,31],[29,30],[32,35],[33,34],[36,37],[38,39],[40,42],[41,43],[48,50],[49,51],[56,59],[57,58],[60,61],[62,63],[64,86],[65,87],[66,84],[67,85],[68,82],[69,83],[70,80],[71,81],[72,93],[73,92],[74,95],[75,94],[76,89],[77,88],[78,91],[79,90]],
[[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],[64,66],[65,67],[68,70],[69,71],[72,74],[73,75],[76,78],[77,79],[80,82],[81,83],[84,86],[85,87],[88,90],[89,91],[92,94],[93,95]],
[[0,4,2,6],[1,5,3,7],[8,12,10,14],[9,13,11,15],[16,20,18,22],[17,21,19,23],[24,28,26,30],[25,29,27,31],[32,36,34,38],[33,37,35,39],[40,44,42,46],[41,45,43,47],[48,52,50,54],[49,53,51,55],[56,60,58,62],[57,61,59,63],[64,68,66,70],[65,69,67,71],[72,76,74,78],[73,77,75,79],[80,84,82,86],[81,85,83,87],[88,92,90,94],[89,93,91,95]],
[[0,8],[1,9],[2,10],[3,11],[4,12],[5,13],[6,14],[7,15],[16,25],[17,24],[18,27],[19,26],[20,29],[21,28],[22,31],[23,30],[32,42],[33,43],[34,40],[35,41],[36,46],[37,47],[38,44],[39,45],[48,59],[49,58],[50,57],[51,56],[52,63],[53,62],[54,61],[55,60],[64,93],[65,92],[66,95],[67,94],[68,91],[69,90],[70,89],[71,88],[72,87],[73,86],[74,85],[75,84],[76,81],[77,80],[78,83],[79,82]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d a 
() c b 
() cd ab 
() bd ac 
() bd abc 

Design No 19(for Input Group of Order 16 and Index 4) Group Size 16 B4F747FB F818DC2F
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d a 
() c b 
() cd ab 
() bd ac 
() bd abcd 

Design No 20(for Input Group of Order 16 and Index 4) Group Size 96 77CDEAC9 289ED20B
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],[32,34],[33,35],[40,43],[41,42],[44,45],[46,47],[48,51],[49,50],[52,53],[54,55],[56,58],[57,59],[64,87],[65,86],[66,85],[67,84],[68,83],[69,82],[70,81],[71,80],[72,92],[73,93],[74,94],[75,95],[76,88],[77,89],[78,90],[79,91]],
[[1,8,9],[3,10,11],[5,12,13],[7,14,15],[16,25,17],[18,27,19],[20,29,21],[22,31,23],[33,42,43],[35,40,41],[37,46,47],[39,44,45],[48,74,64],[49,85,92],[50,72,66],[51,87,94],[52,78,68],[53,83,90],[54,76,70],[55,81,88],[56,73,95],[57,86,67],[58,75,93],[59,84,65],[60,77,89],[61,80,71],[62,79,91],[63,82,69]],
[[0,1],[2,3],[4,7],[5,6],[12,14],[13,15],[20,22],[21,23],[24,25],[26,27],[28,31],[29,30],[32,35],[33,34],[36,37],[38,39],[40,42],[41,43],[48,50],[49,51],[56,59],[57,58],[60,61],[62,63],[64,86],[65,87],[66,84],[67,85],[68,82],[69,83],[70,80],[71,81],[72,93],[73,92],[74,95],[75,94],[76,89],[77,88],[78,91],[79,90]],
[[0,2],[1,3],[8,11],[9,10],[12,13],[14,15],[16,19],[17,18],[20,21],[22,23],[24,26],[25,27],[36,38],[37,39],[40,41],[42,43],[44,47],[45,46],[48,49],[50,51],[52,55],[53,54],[60,62],[61,63],[64,85],[65,84],[66,87],[67,86],[68,81],[69,80],[70,83],[71,82],[72,94],[73,95],[74,92],[75,93],[76,90],[77,91],[78,88],[79,89]],
[[0,4,2,6],[1,5,3,7],[8,12,10,14],[9,13,11,15],[16,20,18,22],[17,21,19,23],[24,28,26,30],[25,29,27,31],[32,36,34,38],[33,37,35,39],[40,44,42,46],[41,45,43,47],[48,52,50,54],[49,53,51,55],[56,60,58,62],[57,61,59,63],[64,68,66,70],[65,69,67,71],[72,76,74,78],[73,77,75,79],[80,84,82,86],[81,85,83,87],[88,92,90,94],[89,93,91,95]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d a 
() c b 
() cd ab 
() bd acd 
() bd abcd 

Design No 21(for Input Group of Order 16 and Index 4) Group Size 32 A46FF07C 2ACE8BF5
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],[32,34],[33,35],[36,37],[38,39],[40,43],[41,42],[48,51],[49,50],[56,58],[57,59],[60,61],[62,63],[64,87],[65,86],[66,85],[67,84],[68,82],[69,83],[70,80],[71,81],[72,92],[73,93],[74,94],[75,95],[76,89],[77,88],[78,91],[79,90]],
[[0,1],[2,3],[4,6],[5,7],[12,15],[13,14],[20,23],[21,22],[24,25],[26,27],[28,30],[29,31],[32,35],[33,34],[40,42],[41,43],[44,45],[46,47],[48,50],[49,51],[52,53],[54,55],[56,59],[57,58],[64,86],[65,87],[66,84],[67,85],[68,83],[69,82],[70,81],[71,80],[72,93],[73,92],[74,95],[75,94],[76,88],[77,89],[78,90],[79,91]],
[[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],[64,66],[65,67],[68,70],[69,71],[72,74],[73,75],[76,78],[77,79],[80,82],[81,83],[84,86],[85,87],[88,90],[89,91],[92,94],[93,95]],
[[0,4,1,5],[2,6,3,7],[8,13,9,12],[10,15,11,14],[16,21,17,20],[18,23,19,22],[24,28,25,29],[26,30,27,31],[32,38,33,39],[34,36,35,37],[40,47,41,46],[42,45,43,44],[48,55,49,54],[50,53,51,52],[56,62,57,63],[58,60,59,61],[64,81,65,80],[66,83,67,82],[68,86,69,87],[70,84,71,85],[72,90,73,91],[74,88,75,89],[76,93,77,92],[78,95,79,94]],
[[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],[32,42],[33,43],[34,40],[35,41],[36,47],[37,46],[38,45],[39,44],[48,59],[49,58],[50,57],[51,56],[52,62],[53,63],[54,60],[55,61],[64,93],[65,92],[66,95],[67,94],[68,90],[69,91],[70,88],[71,89],[72,87],[73,86],[74,85],[75,84],[76,80],[77,81],[78,82],[79,83]]
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d a 
() c ab 
() cd b 
() b ac 
() bd abc 

Design No 22(for Input Group of Order 16 and Index 4) Group Size 16 84E5ECC4 1C7C42FD
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d a 
() c ab 
() cd b 
() b ac 
() bd abcd 

Design No 23(for Input Group of Order 16 and Index 4) Group Size 16 8798F550 434B7D22
Block Intersection Formula 
{(0)^40 (1)^36 (2)^3 (3)^1 }^80 
Initial Blocks, in the group representation:
() d a 
() c ab 
() cd b 
() b abc 
() bd ac