TA Algorithm to find a lean design Runs n=36, Factors s=14. Initial Design: 1 1 2 2 3 3 2 2 3 3 2 2 3 3 2 2 2 2 3 3 3 3 2 2 3 3 2 2 1 2 3 3 2 2 2 2 3 3 3 3 2 2 2 1 3 3 2 2 3 3 2 2 2 2 3 3 1 1 2 3 2 3 3 1 3 1 1 2 1 2 2 2 2 3 2 3 1 3 1 3 2 1 2 1 1 2 3 2 3 2 3 1 3 1 2 1 2 1 2 1 3 2 3 2 1 3 1 3 1 2 1 2 1 1 2 3 3 2 1 2 2 1 3 1 1 3 2 2 2 3 3 2 2 1 1 2 1 3 3 1 1 2 3 2 2 3 1 2 2 1 1 3 3 1 2 1 3 2 2 3 2 1 1 2 3 1 1 3 1 1 3 3 1 1 3 3 1 1 3 3 1 1 2 2 3 3 1 1 1 1 3 3 1 1 3 3 1 2 1 1 3 3 3 3 1 1 1 1 3 3 2 1 1 1 3 3 1 1 3 3 3 3 1 1 1 1 3 1 3 1 1 2 1 2 2 3 2 3 2 2 3 1 3 1 2 1 2 1 3 2 3 2 1 2 1 3 1 3 1 2 1 2 3 2 3 2 2 1 1 3 1 3 2 1 2 1 2 3 2 3 1 1 3 1 1 3 2 3 3 2 1 2 2 1 2 2 3 1 1 3 3 2 2 3 2 1 1 2 1 2 1 3 3 1 2 3 3 2 2 1 1 2 2 1 1 3 3 1 3 2 2 3 1 2 2 1 1 1 1 1 2 2 1 1 2 2 1 1 2 2 2 2 1 1 2 2 2 2 1 1 2 2 1 1 1 2 2 2 1 1 1 1 2 2 2 2 1 1 2 1 2 2 1 1 2 2 1 1 1 1 2 2 1 1 1 2 1 2 2 3 2 3 3 1 3 1 2 2 1 2 1 2 3 2 3 2 1 3 1 3 1 2 2 1 2 1 2 3 2 3 1 3 1 3 2 1 2 1 2 1 3 2 3 2 3 1 3 1 1 1 1 2 2 1 3 1 1 3 2 3 3 2 2 2 1 2 2 1 1 3 3 1 3 2 2 3 1 2 2 1 1 2 3 1 1 3 3 2 2 3 2 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 3 3 3 1 3 1 1 1 1 3 3 1 1 2 1 3 2 3 3 2 1 1 3 2 1 2 2 1 1 1 3 1 2 3 3 1 2 2 3 2 2 2 2 3 1 1 3 3 2 3 2 2 1 1 1 2 3 1 1 3 3 3 3 1 1 1 1 3 1 1 1 1 1 2 1 2 2 2 2 1 1 2 2 1 3 3 2 3 1 2 2 3 1 1 2 1 2 2 1 3 3 1 1 1 3 3 3 1 1 3 1 2 2 3 2 2 1 3 1 1 2 1 3 3 2 2 3 2 3 2 1 3 1 3 1 2 1 2 2 1 3 2 1 1 1 2 2 1 3 2 3 3 1 1 3 3 1 1 2 3 1 2 3 1 2 2 1 2 2 3 3 2 2 2 2 3 3 3 3 2 2 2 2 1 2 1 3 2 3 2 3 1 3 1 1 1 1 1 2 2 3 1 2 3 1 2 3 3 2 1 2 2 2 1 2 1 2 1 1 1 1 2 1 2 1 2 1 1 3 2 3 3 1 3 2 2 2 2 1 2 3 3 2 2 1 2 1 1 3 3 1 1 1 2 3 2 3 3 2 1 3 1 2 1 1 2 3 2 1 2 2 1 3 3 2 1 3 1 2 1 1 1 1 3 1 3 1 3 3 3 3 1 2 1 2 2 1 2 3 1 1 2 3 3 1 3 2 2 3 2 2 3 3 3 2 2 2 3 3 2 2 1 1 3 2 2 2 3 3 2 1 3 1 1 1 1 2 3 1 3 1 1 3 2 1 2 3 2 2 2 3 1 2 2 1 1 3 1 3 3 2 2 1 2 2 1 3 1 1 3 2 2 1 3 2 3 1 1 2 2 3 3 1 2 3 1 2 3 1 1 1 1 2 2 2 3 2 3 3 3 3 2 2 3 1 2 1 2 2 1 1 1 1 2 2 2 2 1 2 1 3 3 3 2 3 2 3 2 2 2 2 3 2 2 1 3 1 3 2 1 2 1 2 3 2 3 2 1 2 1 3 3 3 1 1 3 2 1 2 2 2 2 2 1 1 2 2 2 1 1 1 2 2 1 1 1 3 1 2 1 2 2 1 3 2 3 1 3 1 2 3 1 3 3 2 1 2 2 3 2 1 1 Runs Permutation: 13 7 20 22 15 25 8 14 11 6 36 21 3 30 33 28 35 10 5 31 16 32 2 12 17 34 19 9 1 27 4 18 24 26 29 23 Factors Permutation: 1 2 8 3 4 5 7 6 14 10 9 11 12 13 Max Product Det: 2.7079e-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 0 1 1 0 -1 -1 1 0 -1 0 -1 -1 2 -1 -1 2 -1 -1 -1 2 -1 2 1 1 -1 -1 -1 1 -1 0 1 1 -1 0 0 1 0 -1 -1 -1 -1 2 -1 -1 -1 2 2 -1 2 1 1 1 0 1 -1 -1 1 1 0 1 0 0 -1 -1 2 -1 -1 -1 -1 -1 2 -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 0 -1 0 0 0 0 -1 -1 0 -1 -1 -1 2 -1 2 2 2 2 -1 -1 2 1 1 -1 1 1 0 1 -1 0 0 1 -1 -1 0 -1 -1 -1 2 -1 -1 2 2 -1 -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 0 1 0 0 -1 1 -1 -1 0 -1 1 1 2 -1 2 2 -1 -1 -1 -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 0 -1 -1 -1 0 0 -1 1 0 1 1 -1 2 -1 -1 -1 2 2 -1 -1 2 -1 -1 1 -1 -1 1 1 -1 -1 0 1 -1 0 1 -1 0 0 -1 -1 -1 -1 2 -1 -1 2 -1 -1 2 2 1 -1 1 0 1 1 0 0 0 0 1 1 1 1 0 2 -1 -1 2 2 2 2 -1 -1 -1 -1 2 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 0 0 1 -1 0 1 -1 0 1 1 -1 -1 2 2 -1 -1 2 -1 -1 2 -1 -1 1 1 -1 0 0 0 -1 0 -1 0 -1 -1 -1 -1 0 2 2 2 -1 2 -1 2 -1 -1 -1 -1 2 1 -1 1 -1 0 -1 -1 1 0 1 1 -1 1 0 0 -1 2 -1 -1 -1 2 -1 -1 -1 -1 2 2 1 1 1 -1 0 1 1 0 0 -1 0 -1 -1 1 1 -1 2 -1 -1 2 2 -1 2 -1 -1 -1 -1 1 -1 -1 -1 0 1 0 1 1 0 -1 1 -1 0 -1 -1 2 -1 2 -1 -1 2 -1 -1 -1 2 -1 1 -1 1 1 0 -1 0 0 -1 1 1 0 -1 1 -1 -1 2 -1 2 2 -1 -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 0 0 -1 0 1 -1 -1 0 1 1 -1 1 2 2 -1 2 -1 -1 -1 2 -1 -1 -1 -1 1 1 1 1 0 0 1 1 1 0 0 0 1 1 0 -1 2 2 -1 -1 -1 2 2 2 -1 -1 2 1 1 -1 -1 1 0 0 0 1 1 0 -1 1 -1 -1 -1 -1 2 2 2 -1 -1 2 -1 -1 -1 -1 1 -1 -1 0 1 -1 1 -1 -1 1 0 -1 0 1 0 2 -1 -1 -1 -1 -1 -1 2 -1 2 -1 2 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 0 -1 1 -1 -1 1 0 0 -1 1 0 1 2 -1 -1 -1 -1 -1 2 2 -1 -1 2 -1 1 -1 -1 0 0 1 1 -1 0 1 -1 0 1 -1 -1 2 2 -1 -1 -1 2 -1 -1 2 -1 -1 -1 1 -1 -1 0 0 0 1 0 1 1 1 1 0 0 1 2 2 2 -1 2 -1 -1 -1 -1 2 2 -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 1 0 1 0 0 0 0 1 -1 -1 -1 2 -1 2 -1 2 2 2 2 -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 0 -1 1 1 1 -1 -1 1 0 -1 0 0 2 -1 -1 -1 -1 -1 -1 -1 2 -1 2 2 1 1 1 0 -1 -1 0 0 0 -1 -1 -1 0 0 -1 2 -1 -1 2 2 2 -1 -1 -1 2 2 -1 1 -1 -1 1 -1 0 -1 0 0 -1 1 0 1 -1 1 -1 -1 2 -1 2 2 -1 -1 2 -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 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.142876 0.914610 4.373448 Top 6 Left 6 Corner: 0.159988 0.832889 4.702669 Top 7 Left 7 Corner: 0.191735 0.857601 5.474952 Top 8 Left 8 Corner: 0.206299 0.785266 5.764243 Top 9 Left 9 Corner: 0.218295 0.781230 5.997251 Top 10 Left 10 Corner: 0.225703 0.736850 6.117527 Top 11 Left 11 Corner: 0.241303 0.713860 6.468426 Top 12 Left 12 Corner: 0.248827 0.679501 6.608940 Top 13 Left 13 Corner: 0.252515 0.660503 6.654787 Top 14 Left 14 Corner: 0.277890 0.671026 7.274754 Top 15 Left 15 Corner: 0.302218 0.694168 7.865930 Top 16 Left 16 Corner: 0.307663 0.675169 8.533419 Top 17 Left 17 Corner: 0.319136 0.668372 9.362531 Top 18 Left 18 Corner: 0.342099 0.675664 10.549500 Top 19 Left 19 Corner: 0.350726 0.657686 11.309157 Top 20 Left 20 Corner: 0.382081 0.681137 12.825101 Top 21 Left 21 Corner: 0.418707 0.704018 14.574653 Top 22 Left 22 Corner: 0.444128 0.710185 15.978749 Top 23 Left 23 Corner: 0.462058 0.714590 17.132907 Top 24 Left 24 Corner: 0.494188 0.734355 18.838020 Top 25 Left 25 Corner: 0.537737 0.771846 21.026186 Top 26 Left 26 Corner: 0.555976 0.777316 22.255862 Top 27 Left 27 Corner: 0.582972 0.780353 23.849453 Top 28 Left 27 Corner: 0.639171 0.824620 26.148579 Top 29 Left 27 Corner: 0.679657 0.845791 27.804857 Top 30 Left 27 Corner: 0.722156 0.868200 29.543474 Top 31 Left 27 Corner: 0.766511 0.891227 31.358071 Top 32 Left 27 Corner: 0.812362 0.914454 33.233838 Top 33 Left 27 Corner: 0.856137 0.934541 35.024664 Top 34 Left 27 Corner: 0.901993 0.955373 36.900647 Top 35 Left 27 Corner: 0.949952 0.977270 38.862641 Top 36 Left 27 Corner: 1.000000 1.000000 40.910127 Det Product: 2.707854466661814e-013 0.0003184124023130232 1.828577434055341e+036 ============================================ Expanded Matrix for initial design: 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 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 0 0 1 -1 0 0 -1 -1 -1 -1 -1 -1 2 2 -1 -1 2 2 -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 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 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 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 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 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 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 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 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 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 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 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: 0.075053 0.611257 2.297397 Top 6 Left 6 Corner: 0.000322 0.001642 0.000000 Top 7 Left 7 Corner: 0.000005 0.000024 0.000000 Top 8 Left 8 Corner: 0.000000 0.000000 0.000000 Top 9 Left 9 Corner: 0.002906 0.012582 0.000000 Top 10 Left 10 Corner: 0.003842 0.014434 0.000000 Top 11 Left 11 Corner: 0.000369 0.001224 0.000000 Top 12 Left 12 Corner: 0.000772 0.001471 0.000000 Top 13 Left 13 Corner: 0.017945 0.042219 0.000000 Top 14 Left 14 Corner: 0.238388 0.618877 6.240637 Top 15 Left 15 Corner: 0.261587 0.613696 6.808412 Top 16 Left 16 Corner: 0.297050 0.637966 8.239069 Top 17 Left 17 Corner: 0.306289 0.621862 8.985663 Top 18 Left 18 Corner: 0.051470 0.098262 1.447471 Top 19 Left 19 Corner: 0.009379 0.021105 0.000000 Top 20 Left 20 Corner: 0.012474 0.023022 0.000000 Top 21 Left 21 Corner: 0.013889 0.025701 0.000000 Top 22 Left 22 Corner: 0.016790 0.027810 0.000000 Top 23 Left 23 Corner: 0.022319 0.036688 0.000000 Top 24 Left 24 Corner: 0.029520 0.045195 1.020496 Top 25 Left 25 Corner: 0.132189 0.200885 5.163542 Top 26 Left 26 Corner: 0.555976 0.771973 22.255862 Top 27 Left 27 Corner: 0.582972 0.778546 23.849453 Top 28 Left 27 Corner: 0.639171 0.822726 26.148579 Top 29 Left 27 Corner: 0.679657 0.844607 27.804857 Top 30 Left 27 Corner: 0.722156 0.867554 29.543474 Top 31 Left 27 Corner: 0.766511 0.890968 31.358071 Top 32 Left 27 Corner: 0.812362 0.914702 33.233838 Top 33 Left 27 Corner: 0.856137 0.934540 35.024664 Top 34 Left 27 Corner: 0.901993 0.955511 36.900647 Top 35 Left 27 Corner: 0.949952 0.977270 38.862641 Top 36 Left 27 Corner: 1.000000 1.000000 40.910127 Det Product: 5.1356e-047+8.8806e-047i 0+0i 0+0i