Plackett and Burman design in 16 runs
1 1
1 1
1 1
1 1
1 1
1 1 1
1 1
1 1
1 1
1 1 1
-1 -1 -1
-1 -1 -1 -1 -1
1 1
1 -1 -1
-1 -1
1 1
1 1 -1 -1
-1 -1
1 1
1 -1 -1
-1 -1 -1
-1 -1 -1
1 1 1 1
1 -1
-1 1
1 -1 -1
1 1 -1
-1 1 1
-1 -1
1 -1
-1 1
1 -1 -1
-1 -1
1 1 -1
-1 1 1
1 -1
-1 -1 -1
1 1
1 1 -1
-1 -1 -1
1 1
1 -1
-1 -1 -1
1 1 -1
-1 1
1 1 1
-1 -1
-1 1
-1 1
-1 1
-1 1
-1 1
-1 1 -1
1 -1
-1 1
-1 1
-1 1 -1
-1 1
-1 1
-1 1 -1 1
-1 1
-1 -1 1
-1 1
1 -1 1
-1 -1 1
-1 1
-1 1
-1 -1 1
-1 1
-1 1
-1 1
1 -1 1 -1
-1 -1
1 1 -1
-1 1
1 -1 -1
1 1 -1
-1 1
-1 -1
1 1 -1
-1 1
-1 1
1 -1 -1
1 1 -1
-1 -1
1 -1
1 1
-1 1 -1
-1 1
-1 1 1 -1
-1 -1
1 -1
1 1 -1
-1 1
1 -1 1 -1
-1 1
Designs with 7 factors
There are 6 non-isomorphic designs
for designs with 7 factors
The generalised word counts for each of these designs
Design 1
2 3 4
5 6
b_1(1) 0 0
0 0 0 0
b_2(2) 0 0
0 0 0 0
b_3(3) 7 4
3 3 2 0
b_4(4) 7 3
3 2 3 7
b_5(5) 0 0
0 1 2 0
b_6(6) 0 0
0 1 0 0
b_7(7) 1 0
1 0 0 0
Details of the designs
Plan for design 1
1 1
1 1
1 1 1
1 1
1 1
1 1 1
1 1
1 -1 -1
-1 -1
1 1
1 -1 -1
-1 -1
1 -1
-1 1
1 -1 -1
1 -1
-1 1
1 -1 -1
1 -1
-1 -1 -1
1 1
1 -1
-1 -1 -1
1 1
-1 1
-1 1
-1 1 -1
-1 1
-1 1
-1 1 -1
-1 1
-1 -1 1
-1 1
-1 1
-1 -1 1
-1 1
-1 -1
1 1 -1
-1 1
-1 -1
1 1 -1
-1 1
-1 -1
1 -1
1 1 -1
-1 -1
1 -1
1 1 -1
Generalised word counts for this design are:
B 1 : 0
B 2 : 0
B 3 : 7
B 4 : 7
B 5 : 0
B 6 : 0
B 7 : 1
=====================
Plan for design 2
1 1
1 1
1 1 1
1 1
1 1
1 1 -1
1 1
1 -1 -1
-1 1
1 1
1 -1 -1
-1 -1
1 -1
-1 1
1 -1 1
1 -1
-1 1
1 -1 -1
1 -1
-1 -1 -1
1 1
1 -1
-1 -1 -1
1 -1
-1 1
-1 1
-1 1 1
-1 1
-1 1
-1 1 -1
-1 1
-1 -1 1
-1 1
-1 1
-1 -1 1
-1 -1
-1 -1
1 1 -1
-1 1
-1 -1
1 1 -1
-1 -1
-1 -1
1 -1
1 1 1
-1 -1
1 -1
1 1 -1
Generalised word counts for this design are:
B 1 : 0
B 2 : 0
B 3 : 4
B 4 : 3
B 5 : 0
B 6 : 0
B 7 : 0
=====================
Plan for design 3
1 1
1 1
1 1 1
1 1
1 1 1
-1 -1
1 1
1 -1 -1
1 1
1 1
1 -1 -1
-1 -1
1 -1
-1 1
1 1 1
1 -1
-1 1
1 -1 -1
1 -1
-1 -1 -1
1 1
1 -1
-1 -1 -1
-1 -1
-1 1
-1 1
-1 1 -1
-1 1
-1 1 -1
-1 1
-1 1
-1 -1
1 1 -1
-1 1
-1 -1 1
-1 1
-1 -1
1 1
-1 1 -1
-1 -1
1 1 -1
-1 1
-1 -1
1 -1
1 1 -1
-1 -1
1 -1 1
-1 1
Generalised word counts for this design are:
B 1 : 0
B 2 : 0
B 3 : 3
B 4 : 3
B 5 : 0
B 6 : 0
B 7 : 1
=====================
Plan for design 4
1 1
1 1
1 1 1
1 1
1 1 1
-1 -1
1 1
1 -1 -1
1 1
1 1
1 -1 -1
-1 -1
1 -1
-1 1
1 1 -1
1 -1
-1 1
1 -1 1
1 -1
-1 -1 -1
1 -1
1 -1
-1 -1 -1
-1 1
-1 1
-1 1
-1 1 1
-1 1
-1 1 -1
-1 -1
-1 1
-1 -1
1 1 1
-1 1
-1 -1 1
-1 -1
-1 -1
1 1
-1 1 -1
-1 -1
1 1 -1
-1 1
-1 -1
1 -1
1 1 -1
-1 -1
1 -1 1
-1 1
Generalised word counts for this design are:
B 1 : 0
B 2 : 0
B 3 : 3
B 4 : 2
B 5 : 1
B 6 : 1
B 7 : 0
=====================
Plan for design 5
1 1
1 1
1 1 1
1 1
1 1 1
-1 -1
1 1
1 -1 -1
1 -1
1 1
1 -1 -1
-1 1
1 -1
-1 1
1 1 -1
1 -1
-1 1
1 -1 1
1 -1
-1 -1 -1
1 1
1 -1
-1 -1 -1
-1 -1
-1 1
-1 1
-1 1 1
-1 1
-1 1 -1
-1 -1
-1 1
-1 -1
1 1 -1
-1 1
-1 -1 1
-1 1
-1 -1
1 1
-1 1 -1
-1 -1
1 1 -1
-1 1
-1 -1
1 -1
1 1 1
-1 -1
1 -1 1
-1 -1
Generalised word counts for this design are:
B 1 : 0
B 2 : 0
B 3 : 2
B 4 : 3
B 5 : 2
B 6 : 0
B 7 : 0
=====================
Plan for design 6
1 1
1 1
1 1 1
1 1
1 1 -1
-1 -1
1 1
-1 -1
1 1 -1
1 1
-1 -1 -1
-1 1
1 -1
1 -1 1
-1 1
1 -1
1 -1 -1
1 -1
1 -1
-1 1
1 -1 -1
1 -1
-1 1
-1 1 1
-1 1
1 -1 1
-1 -1
-1 1
1 -1 -1
1 1
-1 1
-1 1
1 -1 1
-1 1
-1 1
-1 1 -1
-1 -1
1 1
1 1 -1
-1 -1
1 1 -1
-1 1
-1 -1 -1
-1 1
1 1
-1 -1 -1
-1 -1 -1 -1
Generalised word counts for this design are:
B 1 : 0
B 2 : 0
B 3 : 0
B 4 : 7
B 5 : 0
B 6 : 0
B 7 : 0
=====================
The number of total eligible submodels, obeying functional marginality,
of the second-order maxiaml models for two-level designs with 7 factors
in 16 runs
delta_00 = 620772
The values of the numbers of submodels with at least main effects of i
factors and j two-factor interactions of these i factors
delta_10 = 585647
delta_20 = 551972
delta_21 = 207996
delta_31 = 192828
delta_32 = 68646
delta_42 = 62016