TA Algorithm to find a lean design Runs n=36, Factors s=16. Initial Design: 1 1 1 1 2 2 3 3 2 2 3 3 2 2 3 3 2 2 2 1 2 2 3 3 3 3 2 2 3 3 2 2 1 2 1 2 3 3 2 2 2 2 3 3 3 3 2 2 2 1 2 2 3 3 2 2 3 3 2 2 2 2 3 3 1 1 1 2 2 3 2 3 3 1 3 1 1 2 1 2 2 2 1 1 2 3 2 3 1 3 1 3 2 1 2 1 1 2 2 1 3 2 3 2 3 1 3 1 2 1 2 1 2 1 2 2 3 2 3 2 1 3 1 3 1 2 1 2 1 1 2 1 2 3 3 2 1 2 2 1 3 1 1 3 2 2 1 2 2 3 3 2 2 1 1 2 1 3 3 1 1 2 2 2 3 2 2 3 1 2 2 1 1 3 3 1 2 1 1 1 3 2 2 3 2 1 1 2 3 1 1 3 1 1 1 1 3 3 1 1 3 3 1 1 3 3 1 1 2 2 2 1 3 3 1 1 1 1 3 3 1 1 3 3 1 2 1 2 1 1 3 3 3 3 1 1 1 1 3 3 2 1 2 2 1 1 3 3 1 1 3 3 3 3 1 1 1 1 1 2 3 1 3 1 1 2 1 2 2 3 2 3 2 2 1 1 3 1 3 1 2 1 2 1 3 2 3 2 1 2 2 1 1 3 1 3 1 2 1 2 3 2 3 2 2 1 2 2 1 3 1 3 2 1 2 1 2 3 2 3 1 1 2 1 3 1 1 3 2 3 3 2 1 2 2 1 2 2 1 2 3 1 1 3 3 2 2 3 2 1 1 2 1 2 2 2 1 3 3 1 2 3 3 2 2 1 1 2 2 1 1 1 1 3 3 1 3 2 2 3 1 2 2 1 1 1 1 1 1 1 2 2 1 1 2 2 1 1 2 2 2 2 2 1 1 1 2 2 2 2 1 1 2 2 1 1 1 2 1 2 2 2 1 1 1 1 2 2 2 2 1 1 2 1 2 2 2 2 1 1 2 2 1 1 1 1 2 2 1 1 1 2 1 2 1 2 2 3 2 3 3 1 3 1 2 2 1 1 1 2 1 2 3 2 3 2 1 3 1 3 1 2 2 1 2 1 2 1 2 3 2 3 1 3 1 3 2 1 2 2 2 1 2 1 3 2 3 2 3 1 3 1 1 1 2 1 1 2 2 1 3 1 1 3 2 3 3 2 2 2 1 2 1 2 2 1 1 3 3 1 3 2 2 3 1 2 2 2 2 1 1 2 3 1 1 3 3 2 2 3 2 1 1 1 2 1 1 2 1 3 3 1 2 3 3 2 Criterion: maximize Det(X(5)'X(5))*...*Det(X(36)'X(36)) Search Type:(b) - f1(x1) ... f1(xs) f2(x1) ... f2(xs) Result Design: 1 1 1 1 3 1 1 3 3 1 1 3 3 1 1 3 1 2 1 2 1 1 3 3 1 3 1 3 1 3 3 1 1 2 2 1 1 2 1 2 3 3 1 1 3 2 3 2 2 1 2 2 3 3 3 3 2 2 1 1 1 2 1 2 2 2 1 1 3 1 3 1 1 1 2 2 3 2 3 2 2 1 1 1 1 3 3 2 3 1 2 3 1 1 2 2 2 1 2 2 1 1 1 1 3 3 2 2 2 3 2 3 2 2 1 2 3 3 1 2 1 3 2 3 2 2 1 1 1 1 2 1 1 3 2 1 2 1 1 3 2 2 3 3 2 1 1 1 2 1 1 3 1 2 3 1 2 2 3 3 1 1 1 1 2 3 3 2 2 3 3 2 2 3 3 2 1 2 2 2 1 2 3 3 3 1 3 2 2 2 1 1 2 2 2 1 2 2 3 3 2 3 2 3 3 2 2 3 2 2 2 1 3 3 1 1 3 1 3 1 1 3 3 1 1 1 2 1 3 2 1 3 1 3 3 2 1 1 2 2 2 1 2 2 3 2 2 3 3 2 2 3 2 3 3 2 2 2 1 2 2 2 3 1 3 2 1 2 1 1 3 3 2 1 2 2 2 1 1 2 2 1 1 2 1 2 2 1 2 1 1 1 3 2 2 1 2 3 1 2 3 3 1 1 1 2 2 2 3 1 2 2 2 3 2 1 1 1 3 3 2 2 1 1 1 2 1 2 2 2 3 3 1 3 1 3 1 1 1 2 1 3 1 3 2 2 2 2 3 1 3 1 1 2 2 1 3 1 3 1 2 2 3 3 2 1 2 1 1 2 2 1 2 3 2 3 1 1 2 2 1 3 1 3 1 2 1 2 2 2 1 1 2 1 2 1 2 1 1 2 2 1 2 2 2 2 2 2 1 1 3 3 3 1 3 1 1 1 1 2 2 1 2 1 3 3 3 3 1 2 1 2 1 2 1 2 3 3 2 2 3 2 3 2 3 2 2 3 1 1 1 1 1 2 2 1 1 2 2 1 1 2 2 1 2 2 1 1 2 3 2 3 3 3 1 1 2 1 2 1 1 1 1 2 3 2 3 2 1 1 1 1 2 3 2 3 1 1 2 1 2 1 3 2 3 2 2 1 3 3 1 1 1 2 2 2 2 3 1 1 1 2 1 3 3 3 2 2 2 2 1 2 1 1 2 3 2 1 3 1 3 3 2 2 2 2 2 1 1 1 2 2 1 2 1 2 2 1 1 2 2 1 2 2 1 3 3 1 1 3 3 1 3 1 1 3 Runs Permutation: 13 15 19 8 18 24 20 22 33 36 1 23 2 14 21 4 10 28 12 11 30 29 7 31 27 32 5 3 25 6 17 9 35 34 26 16 Factors Permutation: 1 2 3 4 5 12 7 10 6 8 11 9 13 16 15 14 Max Product Det: 6.7964e-013 ============================================ Expanded Matrix: 1 -1 -1 -1 -1 1 -1 -1 1 1 -1 -1 1 1 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 1 -1 1 -1 -1 1 1 -1 1 -1 1 -1 1 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 1 1 -1 -1 0 -1 0 1 1 -1 -1 1 0 1 0 -1 2 -1 2 -1 -1 -1 -1 -1 2 -1 2 1 1 -1 1 1 1 1 1 1 0 0 -1 -1 -1 0 -1 0 -1 -1 -1 -1 2 2 -1 -1 -1 2 -1 2 1 1 1 -1 -1 1 -1 1 -1 -1 -1 0 0 1 0 1 0 -1 -1 -1 -1 -1 -1 2 2 -1 2 -1 2 1 1 -1 -1 -1 -1 1 1 0 1 -1 0 1 -1 -1 0 0 -1 -1 -1 2 -1 -1 2 -1 -1 -1 2 2 1 1 -1 1 1 -1 -1 -1 -1 1 1 0 0 0 1 0 1 -1 -1 -1 -1 -1 -1 2 2 2 -1 2 -1 1 1 1 -1 1 1 1 -1 0 -1 1 0 1 0 0 -1 -1 -1 -1 -1 2 -1 -1 2 -1 2 2 -1 -1 1 -1 -1 1 -1 -1 1 0 -1 0 -1 -1 1 0 0 1 1 -1 -1 2 -1 2 -1 -1 -1 2 2 -1 -1 1 1 -1 -1 -1 0 -1 -1 1 -1 0 1 -1 0 0 1 1 2 -1 -1 -1 -1 2 -1 -1 2 2 -1 -1 1 -1 -1 -1 -1 0 1 1 0 0 1 1 0 0 1 1 0 2 -1 -1 2 2 -1 -1 2 2 -1 -1 2 1 -1 1 1 1 -1 0 1 1 1 -1 1 0 0 0 -1 -1 -1 2 -1 -1 -1 -1 -1 2 2 2 -1 -1 1 1 1 1 -1 0 0 1 1 0 1 0 1 1 0 0 1 2 2 -1 -1 2 -1 2 -1 -1 2 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 0 -1 1 -1 1 1 0 -1 -1 0 0 -1 2 -1 -1 -1 -1 -1 2 -1 -1 2 2 1 1 -1 1 1 1 0 0 1 1 0 0 1 0 1 1 0 -1 2 2 -1 -1 2 2 -1 2 -1 -1 2 1 1 1 -1 1 0 0 1 -1 1 0 -1 0 -1 -1 1 1 2 2 -1 -1 -1 2 -1 2 -1 -1 -1 -1 1 1 -1 1 1 0 -1 -1 0 0 -1 -1 0 -1 0 0 -1 2 -1 -1 2 2 -1 -1 2 -1 2 2 -1 1 1 -1 -1 -1 1 0 0 -1 0 1 -1 0 1 1 -1 -1 -1 2 2 -1 2 -1 -1 2 -1 -1 -1 -1 1 -1 1 1 1 1 -1 0 0 0 1 0 -1 -1 -1 1 1 -1 -1 2 2 2 -1 2 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 0 -1 0 0 0 1 1 -1 1 -1 1 -1 2 -1 2 2 2 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 -1 1 -1 1 0 0 0 0 1 -1 1 -1 -1 -1 -1 -1 2 2 2 2 -1 -1 -1 -1 1 -1 1 1 -1 1 -1 1 -1 0 0 1 1 0 -1 0 -1 -1 -1 -1 -1 2 2 -1 -1 2 -1 2 -1 1 -1 1 1 -1 0 1 0 1 -1 -1 0 0 -1 1 -1 1 2 -1 2 -1 -1 -1 2 2 -1 -1 -1 -1 1 -1 1 -1 1 0 0 -1 -1 0 -1 0 -1 0 -1 -1 0 2 2 -1 -1 2 -1 2 -1 2 -1 -1 2 1 1 -1 1 1 0 0 0 0 -1 -1 1 1 1 -1 1 -1 2 2 2 2 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 0 -1 0 -1 1 1 1 1 -1 0 -1 0 2 -1 2 -1 -1 -1 -1 -1 -1 2 -1 2 1 -1 1 -1 1 1 1 0 0 1 0 1 0 1 0 0 1 -1 -1 2 2 -1 2 -1 2 -1 2 2 -1 1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 2 2 -1 -1 2 2 -1 -1 2 2 -1 1 1 1 -1 -1 0 1 0 1 1 1 -1 -1 0 -1 0 -1 2 -1 2 -1 -1 -1 -1 -1 2 -1 2 -1 1 -1 -1 -1 1 1 0 1 0 -1 -1 -1 -1 0 1 0 1 -1 2 -1 2 -1 -1 -1 -1 2 -1 2 -1 1 -1 -1 1 -1 0 -1 1 0 1 0 0 -1 1 1 -1 -1 2 -1 -1 2 -1 2 2 -1 -1 -1 -1 -1 1 -1 1 1 1 0 1 -1 -1 -1 0 -1 1 1 1 0 0 2 -1 -1 -1 -1 2 -1 -1 -1 -1 2 2 1 1 1 -1 1 -1 -1 0 1 0 -1 1 -1 1 1 0 0 -1 -1 2 -1 2 -1 -1 -1 -1 -1 2 2 1 1 1 1 -1 -1 -1 0 0 -1 0 -1 0 0 -1 -1 0 -1 -1 2 2 -1 2 -1 2 2 -1 -1 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 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.130675 0.940863 4.704316 Top 6 Left 6 Corner: 0.161344 0.904806 5.428835 Top 7 Left 7 Corner: 0.182003 0.852187 5.835377 Top 8 Left 8 Corner: 0.224054 0.880602 6.928203 Top 9 Left 9 Corner: 0.225539 0.809007 6.780502 Top 10 Left 10 Corner: 0.249728 0.802848 7.340486 Top 11 Left 11 Corner: 0.258705 0.768164 7.465473 Top 12 Left 12 Corner: 0.288210 0.788525 8.190158 Top 13 Left 13 Corner: 0.316253 0.818253 8.871004 Top 14 Left 14 Corner: 0.320125 0.770397 8.880156 Top 15 Left 15 Corner: 0.332865 0.767292 9.144836 Top 16 Left 16 Corner: 0.330133 0.717236 8.993512 Top 17 Left 17 Corner: 0.344536 0.712810 9.316164 Top 18 Left 18 Corner: 0.365535 0.725960 10.436657 Top 19 Left 19 Corner: 0.379323 0.712866 11.370594 Top 20 Left 20 Corner: 0.392022 0.709436 12.277582 Top 21 Left 21 Corner: 0.431601 0.743704 14.063725 Top 22 Left 22 Corner: 0.454391 0.747020 15.349656 Top 23 Left 23 Corner: 0.474157 0.748556 16.553131 Top 24 Left 24 Corner: 0.494188 0.744336 17.780723 Top 25 Left 25 Corner: 0.528223 0.761814 19.540033 Top 26 Left 26 Corner: 0.555976 0.767189 21.100282 Top 27 Left 27 Corner: 0.592688 0.787288 23.033420 Top 28 Left 28 Corner: 0.609212 0.784275 24.202766 Top 29 Left 29 Corner: 0.634703 0.789222 25.737823 Top 30 Left 29 Corner: 0.696828 0.837061 28.257041 Top 31 Left 29 Corner: 0.743679 0.864420 30.156908 Top 32 Left 29 Corner: 0.793453 0.893313 32.175305 Top 33 Left 29 Corner: 0.842147 0.919099 34.149863 Top 34 Left 29 Corner: 0.892571 0.945286 36.194611 Top 35 Left 29 Corner: 0.945096 0.972180 38.324544 Top 36 Left 29 Corner: 1.000000 1.000000 40.550974 Det Product: 6.796387197686692e-013 0.001098296129268825 5.470245864629578e+036 ============================================ Expanded Matrix for initial design: 1 -1 -1 -1 -1 0 0 1 1 0 0 1 1 0 0 1 1 2 2 -1 -1 2 2 -1 -1 2 2 -1 -1 1 1 1 1 -1 0 0 1 1 1 1 0 0 1 1 0 0 2 2 -1 -1 -1 -1 2 2 -1 -1 2 2 1 -1 1 -1 1 1 1 0 0 0 0 1 1 1 1 0 0 -1 -1 2 2 2 2 -1 -1 -1 -1 2 2 1 1 -1 1 1 1 1 0 0 1 1 0 0 0 0 1 1 -1 -1 2 2 -1 -1 2 2 2 2 -1 -1 1 -1 -1 -1 1 0 1 0 1 1 -1 1 -1 -1 0 -1 0 2 -1 2 -1 -1 -1 -1 -1 -1 2 -1 2 1 1 1 -1 -1 0 1 0 1 -1 1 -1 1 0 -1 0 -1 2 -1 2 -1 -1 -1 -1 -1 2 -1 2 -1 1 -1 1 1 -1 1 0 1 0 1 -1 1 -1 0 -1 0 -1 -1 2 -1 2 -1 -1 -1 -1 2 -1 2 -1 1 1 -1 1 1 1 0 1 0 -1 1 -1 1 -1 0 -1 0 -1 2 -1 2 -1 -1 -1 -1 -1 2 -1 2 1 -1 -1 1 -1 0 1 1 0 -1 0 0 -1 1 -1 -1 1 2 -1 -1 2 -1 2 2 -1 -1 -1 -1 -1 1 1 1 -1 1 0 1 1 0 0 -1 -1 0 -1 1 1 -1 2 -1 -1 2 2 -1 -1 2 -1 -1 -1 -1 1 -1 1 1 1 1 0 0 1 -1 0 0 -1 -1 1 1 -1 -1 2 2 -1 -1 2 2 -1 -1 -1 -1 -1 1 1 -1 -1 -1 1 0 0 1 0 -1 -1 0 1 -1 -1 1 -1 2 2 -1 2 -1 -1 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 -1 -1 -1 -1 -1 -1 -1 -1 1 -1 -1 -1 1 1 -1 1 -1 -1 0 -1 0 0 1 0 1 -1 -1 -1 -1 -1 2 -1 2 2 -1 2 -1 1 1 1 -1 -1 1 -1 1 -1 0 -1 0 -1 1 0 1 0 -1 -1 -1 -1 2 -1 2 -1 -1 2 -1 2 1 -1 1 1 -1 -1 1 -1 1 -1 0 -1 0 1 0 1 0 -1 -1 -1 -1 -1 2 -1 2 -1 2 -1 2 1 1 -1 1 1 -1 1 -1 1 0 -1 0 -1 0 1 0 1 -1 -1 -1 -1 2 -1 2 -1 2 -1 2 -1 1 -1 -1 1 -1 1 -1 -1 1 0 1 1 0 -1 0 0 -1 -1 -1 -1 -1 2 -1 -1 2 -1 2 2 -1 1 1 1 -1 1 1 -1 -1 1 1 0 0 1 0 -1 -1 0 -1 -1 -1 -1 -1 2 2 -1 2 -1 -1 2 1 -1 1 1 1 -1 1 1 -1 0 1 1 0 0 -1 -1 0 -1 -1 -1 -1 2 -1 -1 2 2 -1 -1 2 1 1 -1 -1 -1 -1 1 1 -1 1 0 0 1 -1 0 0 -1 -1 -1 -1 -1 -1 2 2 -1 -1 2 2 -1 1 -1 -1 -1 -1 -1 -1 0 0 -1 -1 0 0 -1 -1 0 0 -1 -1 2 2 -1 -1 2 2 -1 -1 2 2 1 1 1 1 -1 -1 -1 0 0 0 0 -1 -1 0 0 -1 -1 -1 -1 2 2 2 2 -1 -1 2 2 -1 -1 1 -1 1 -1 1 0 0 -1 -1 -1 -1 0 0 0 0 -1 -1 2 2 -1 -1 -1 -1 2 2 2 2 -1 -1 1 1 -1 1 1 0 0 -1 -1 0 0 -1 -1 -1 -1 0 0 2 2 -1 -1 2 2 -1 -1 -1 -1 2 2 1 -1 -1 -1 1 -1 0 -1 0 0 1 0 1 1 -1 1 -1 -1 2 -1 2 2 -1 2 -1 -1 -1 -1 -1 1 1 1 -1 -1 -1 0 -1 0 1 0 1 0 -1 1 -1 1 -1 2 -1 2 -1 2 -1 2 -1 -1 -1 -1 1 -1 1 1 -1 0 -1 0 -1 0 1 0 1 -1 1 -1 1 2 -1 2 -1 2 -1 2 -1 -1 -1 -1 -1 1 1 -1 1 1 0 -1 0 -1 1 0 1 0 1 -1 1 -1 2 -1 2 -1 -1 2 -1 2 -1 -1 -1 -1 1 -1 -1 1 -1 -1 0 0 -1 1 -1 -1 1 0 1 1 0 -1 2 2 -1 -1 -1 -1 -1 2 -1 -1 2 1 1 1 -1 1 -1 0 0 -1 -1 1 1 -1 1 0 0 1 -1 2 2 -1 -1 -1 -1 -1 -1 2 2 -1 1 -1 1 1 1 0 -1 -1 0 1 -1 -1 1 1 0 0 1 2 -1 -1 2 -1 -1 -1 -1 -1 2 2 -1 1 1 -1 -1 -1 0 -1 -1 0 -1 1 1 -1 0 1 1 0 2 -1 -1 2 -1 -1 -1 -1 2 -1 -1 2 For inital design Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.000000 0.000619 0.000000 Top 6 Left 6 Corner: 0.094355 0.635456 3.174802 Top 7 Left 7 Corner: 0.083956 0.470146 2.691800 Top 8 Left 8 Corner: 0.001586 0.000000 0.000000 Top 9 Left 9 Corner: 0.002658 0.011660 0.000000 Top 10 Left 10 Corner: 0.005167 0.019420 0.000000 Top 11 Left 11 Corner: 0.008004 0.025729 0.000000 Top 12 Left 12 Corner: 0.000730 0.001424 0.000000 Top 13 Left 13 Corner: 0.001309 0.003113 0.000000 Top 14 Left 14 Corner: 0.020301 0.050113 0.000000 Top 15 Left 15 Corner: 0.028475 0.061150 0.000000 Top 16 Left 16 Corner: 0.037649 0.070419 0.000000 Top 17 Left 17 Corner: 0.282304 0.575122 7.633427 Top 18 Left 18 Corner: 0.291413 0.562456 8.320335 Top 19 Left 19 Corner: 0.051174 0.106381 1.563478 Top 20 Left 20 Corner: 0.010725 0.019423 0.000000 Top 21 Left 21 Corner: 0.013151 0.022538 0.000000 Top 22 Left 22 Corner: 0.017330 0.026476 0.000000 Top 23 Left 23 Corner: 0.020600 0.032094 0.000000 Top 24 Left 24 Corner: 0.025364 0.038551 0.000000 Top 25 Left 25 Corner: 0.031436 0.047827 1.057018 Top 26 Left 26 Corner: 0.134961 0.195859 5.058290 Top 27 Left 27 Corner: 0.153138 0.217386 5.741624 Top 28 Left 28 Corner: 0.180884 0.235220 7.294840 Top 29 Left 29 Corner: 0.198252 0.255335 7.682144 Top 30 Left 29 Corner: 0.675155 0.811027 27.378182 Top 31 Left 29 Corner: 0.740592 0.860785 30.031728 Top 32 Left 29 Corner: 0.785621 0.884539 31.857701 Top 33 Left 29 Corner: 0.837440 0.914093 33.959019 Top 34 Left 29 Corner: 0.886977 0.939573 35.967771 Top 35 Left 29 Corner: 0.945096 0.972263 38.324544 Top 36 Left 29 Corner: 1.000000 1.000000 40.550974 Det Product: 0 0 0