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:(a) - f1(x1) f2(x1), ..., f1(xs) f2(xs) Result Design: 2 2 3 2 3 3 3 2 2 2 3 3 2 2 2 2 2 3 1 2 3 2 2 1 1 3 3 1 1 2 1 1 3 2 2 3 2 2 1 3 1 3 1 1 2 3 2 1 3 1 2 2 3 1 1 3 2 1 1 2 2 2 1 1 2 1 1 1 2 2 2 1 2 1 3 1 1 1 2 3 2 3 3 2 1 2 2 2 1 3 3 1 3 3 2 1 2 1 2 1 3 2 1 2 2 2 3 1 3 1 1 3 2 2 3 1 2 3 1 3 3 2 2 1 1 2 1 1 1 3 3 3 1 1 3 1 3 3 1 1 1 2 1 2 1 1 1 2 2 2 2 2 1 1 1 1 1 1 2 1 3 2 3 1 2 3 2 3 1 1 3 1 3 2 1 2 3 3 1 2 2 1 2 1 2 2 3 1 3 3 3 1 1 2 1 2 2 2 2 2 2 3 1 2 1 3 1 3 1 3 2 1 3 1 1 1 3 3 1 3 3 3 1 1 1 2 2 1 1 3 1 3 2 1 3 2 2 3 1 2 3 1 3 3 3 1 1 1 1 1 3 3 1 1 2 2 3 2 1 3 1 2 3 1 3 1 1 1 2 1 1 1 2 2 1 2 1 1 2 2 2 2 1 1 1 2 3 1 3 2 3 2 3 2 1 2 3 2 2 1 2 1 3 2 1 3 3 1 2 2 1 3 1 1 1 3 3 3 1 1 3 3 2 1 2 3 3 3 2 2 3 2 2 2 3 3 2 2 2 1 2 2 2 1 1 1 2 2 1 1 2 1 3 3 1 2 1 1 1 2 2 3 2 3 1 2 2 3 2 2 2 3 3 3 3 3 2 2 1 1 3 3 1 3 2 1 2 3 1 2 1 2 2 1 1 1 2 3 2 2 2 3 3 1 3 1 2 2 3 3 3 1 2 3 2 1 2 1 2 1 1 1 3 2 2 2 3 3 2 3 2 2 3 3 1 2 3 3 2 1 1 2 1 1 3 2 3 2 2 2 1 2 3 1 2 1 1 3 3 2 2 3 1 1 1 2 1 3 2 3 1 1 2 3 3 2 1 2 1 3 3 2 3 2 1 3 2 1 1 2 2 1 1 3 2 3 3 3 1 2 1 2 2 1 Runs Permutation: 2 10 31 9 28 36 7 12 22 13 27 17 21 8 30 16 35 15 29 25 18 11 14 4 26 20 3 5 32 6 1 19 34 33 23 24 Factors Permutation: 1 2 6 4 8 7 5 10 3 9 11 12 13 14 Max Product Det: 1.188e-013 ============================================ Expanded Matrix: 1 1 1 1 -1 0 2 1 -1 1 -1 1 -1 0 2 0 2 0 2 1 -1 1 -1 0 2 0 2 1 1 1 0 2 1 -1 -1 -1 0 2 1 -1 0 2 0 2 -1 -1 -1 -1 1 -1 1 -1 -1 -1 1 -1 1 -1 -1 -1 -1 1 -1 0 2 0 2 1 -1 0 2 0 2 -1 -1 1 -1 -1 -1 1 -1 1 -1 -1 0 2 1 -1 0 2 -1 -1 1 -1 -1 -1 0 2 0 2 1 -1 -1 -1 -1 -1 1 -1 1 1 -1 -1 -1 0 2 0 2 0 2 -1 -1 -1 -1 0 2 -1 -1 -1 -1 -1 -1 0 2 0 2 1 1 -1 0 2 -1 -1 1 -1 -1 -1 -1 -1 -1 -1 0 2 1 -1 0 2 1 -1 1 -1 0 2 1 -1 1 0 2 0 2 -1 -1 1 -1 1 -1 -1 -1 1 -1 1 -1 0 2 -1 -1 0 2 -1 -1 1 1 -1 1 -1 0 2 -1 -1 0 2 0 2 0 2 1 -1 -1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 1 -1 -1 -1 0 2 1 -1 -1 -1 1 -1 1 -1 0 2 0 2 -1 -1 -1 -1 0 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 0 2 -1 -1 -1 -1 -1 -1 0 2 0 2 0 2 0 2 0 2 -1 -1 -1 -1 1 -1 -1 -1 -1 -1 -1 0 2 -1 -1 1 -1 0 2 1 -1 -1 -1 0 2 1 -1 0 2 1 -1 1 -1 -1 1 -1 -1 -1 1 -1 0 2 -1 -1 0 2 1 -1 1 -1 -1 -1 0 2 0 2 -1 -1 1 1 -1 0 2 0 2 1 -1 -1 -1 1 -1 1 -1 1 -1 -1 -1 -1 -1 0 2 -1 -1 0 2 1 1 1 0 2 0 2 0 2 1 -1 -1 -1 0 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 0 2 -1 -1 -1 -1 1 -1 -1 -1 1 -1 0 2 -1 -1 1 -1 0 2 0 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 0 2 0 2 1 -1 0 2 -1 -1 1 -1 -1 -1 0 2 1 -1 -1 -1 1 -1 -1 -1 1 -1 -1 0 2 -1 -1 -1 -1 -1 -1 0 2 0 2 -1 -1 0 2 -1 -1 -1 -1 0 2 0 2 1 1 1 -1 -1 -1 -1 -1 -1 0 2 1 -1 -1 -1 1 -1 0 2 1 -1 0 2 1 -1 0 2 1 -1 1 1 -1 0 2 0 2 -1 -1 0 2 -1 -1 1 -1 0 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 0 2 1 -1 1 -1 1 -1 0 2 0 2 1 -1 0 2 0 2 0 2 1 -1 1 -1 1 1 1 0 2 -1 -1 0 2 0 2 0 2 -1 -1 -1 -1 -1 -1 0 2 0 2 -1 -1 -1 -1 1 1 -1 1 -1 1 -1 -1 -1 0 2 -1 -1 -1 -1 -1 -1 0 2 0 2 1 -1 0 2 1 -1 1 -1 1 0 2 1 -1 0 2 0 2 0 2 1 -1 1 -1 1 -1 1 -1 1 -1 0 2 0 2 1 -1 -1 1 -1 1 -1 -1 -1 1 -1 0 2 -1 -1 0 2 1 -1 -1 -1 0 2 -1 -1 0 2 1 1 -1 -1 -1 -1 -1 0 2 1 -1 0 2 0 2 0 2 1 -1 1 -1 -1 -1 1 -1 -1 -1 1 1 1 1 -1 1 -1 1 -1 -1 -1 0 2 1 -1 0 2 -1 -1 0 2 -1 -1 0 2 -1 -1 1 -1 -1 1 -1 0 2 0 2 0 2 1 -1 1 -1 0 2 1 -1 0 2 0 2 1 -1 1 -1 1 -1 1 1 -1 1 -1 0 2 -1 -1 -1 -1 0 2 -1 -1 -1 -1 1 -1 0 2 1 -1 0 2 1 1 1 -1 -1 0 2 1 -1 -1 -1 0 2 -1 -1 -1 -1 1 -1 1 -1 0 2 0 2 1 -1 1 -1 -1 -1 -1 0 2 -1 -1 1 -1 0 2 1 -1 -1 -1 -1 -1 0 2 1 -1 1 -1 0 2 1 -1 1 -1 -1 1 -1 1 -1 0 2 1 -1 0 2 -1 -1 1 -1 0 2 -1 -1 -1 -1 0 2 1 1 -1 -1 -1 1 -1 0 2 1 -1 1 -1 1 -1 -1 -1 0 2 -1 -1 0 2 0 2 -1 -1 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.123369 0.890044 4.704316 Top 6 Left 6 Corner: 0.139728 0.847434 4.932424 Top 7 Left 7 Corner: 0.157287 0.827261 6.147409 Top 8 Left 8 Corner: 0.171559 0.773105 6.308684 Top 9 Left 9 Corner: 0.196983 0.792879 7.805068 Top 10 Left 10 Corner: 0.206457 0.752819 7.780465 Top 11 Left 11 Corner: 0.235759 0.774812 9.423304 Top 12 Left 12 Corner: 0.251975 0.742972 9.652317 Top 13 Left 13 Corner: 0.268659 0.749153 10.803333 Top 14 Left 14 Corner: 0.271905 0.712676 10.538093 Top 15 Left 15 Corner: 0.296555 0.720612 11.977960 Top 16 Left 16 Corner: 0.314272 0.721756 12.287247 Top 17 Left 17 Corner: 0.330568 0.708420 13.397038 Top 18 Left 18 Corner: 0.357223 0.718457 14.061986 Top 19 Left 19 Corner: 0.355160 0.679776 14.432207 Top 20 Left 20 Corner: 0.381687 0.688447 15.107105 Top 21 Left 21 Corner: 0.413011 0.713687 16.819339 Top 22 Left 22 Corner: 0.429153 0.701707 17.061663 Top 23 Left 23 Corner: 0.442957 0.698096 18.071108 Top 24 Left 24 Corner: 0.493764 0.742674 19.703446 Top 25 Left 25 Corner: 0.522179 0.754513 21.335115 Top 26 Left 26 Corner: 0.573590 0.793983 22.960952 Top 27 Left 27 Corner: 0.582972 0.779628 23.849453 Top 28 Left 27 Corner: 0.639171 0.823375 26.148579 Top 29 Left 27 Corner: 0.679657 0.845001 27.804857 Top 30 Left 27 Corner: 0.722156 0.867715 29.543474 Top 31 Left 27 Corner: 0.766511 0.890968 31.358071 Top 32 Left 27 Corner: 0.812362 0.914404 33.233838 Top 33 Left 27 Corner: 0.856137 0.934254 35.024664 Top 34 Left 27 Corner: 0.901993 0.955235 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: 1.188000928295014e-013 0.0005703088108074593 1.878379574479904e+038 ============================================ Expanded Matrix for initial design: 1 -1 -1 0 2 0 2 1 -1 1 -1 0 2 0 2 1 -1 1 -1 0 2 0 2 1 -1 1 -1 1 1 1 0 2 0 2 1 -1 1 -1 1 -1 1 -1 0 2 0 2 1 -1 1 -1 0 2 0 2 1 -1 1 1 -1 1 -1 0 2 0 2 0 2 0 2 1 -1 1 -1 1 -1 1 -1 0 2 0 2 1 1 -1 1 -1 1 -1 0 2 0 2 1 -1 1 -1 0 2 0 2 0 2 0 2 1 -1 1 -1 1 -1 -1 0 2 1 -1 0 2 1 -1 1 -1 -1 -1 1 -1 -1 -1 -1 -1 0 2 -1 -1 0 2 1 1 1 0 2 1 -1 0 2 1 -1 -1 -1 1 -1 -1 -1 1 -1 0 2 -1 -1 0 2 -1 -1 1 -1 1 1 -1 0 2 1 -1 0 2 1 -1 -1 -1 1 -1 -1 -1 0 2 -1 -1 0 2 -1 -1 1 1 -1 1 -1 0 2 1 -1 0 2 -1 -1 1 -1 -1 -1 1 -1 -1 -1 0 2 -1 -1 0 2 1 -1 -1 0 2 1 -1 1 -1 0 2 -1 -1 0 2 0 2 -1 -1 1 -1 -1 -1 -1 -1 1 -1 1 1 1 0 2 1 -1 1 -1 0 2 0 2 -1 -1 -1 -1 0 2 -1 -1 1 -1 1 -1 -1 -1 1 -1 1 1 -1 0 2 0 2 1 -1 -1 -1 0 2 0 2 -1 -1 -1 -1 1 -1 1 -1 -1 -1 1 1 -1 1 -1 0 2 0 2 1 -1 0 2 -1 -1 -1 -1 0 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 0 2 -1 -1 0 2 0 2 1 -1 0 2 1 -1 1 1 1 1 -1 -1 -1 1 -1 -1 -1 0 2 -1 -1 0 2 -1 -1 1 -1 0 2 1 -1 0 2 1 -1 1 -1 -1 1 -1 -1 -1 1 -1 -1 -1 0 2 -1 -1 0 2 1 -1 0 2 1 -1 0 2 1 1 -1 -1 -1 1 -1 -1 -1 1 -1 0 2 -1 -1 0 2 -1 -1 0 2 1 -1 0 2 1 -1 1 -1 -1 1 -1 -1 -1 -1 -1 1 -1 0 2 1 -1 1 -1 0 2 -1 -1 0 2 0 2 -1 -1 1 1 1 1 -1 -1 -1 -1 -1 1 -1 1 -1 0 2 0 2 1 -1 0 2 -1 -1 -1 -1 0 2 1 -1 1 -1 -1 1 -1 1 -1 -1 -1 0 2 1 -1 1 -1 0 2 0 2 -1 -1 -1 -1 0 2 1 1 -1 -1 -1 1 -1 1 -1 -1 -1 1 -1 0 2 0 2 1 -1 -1 -1 0 2 0 2 -1 -1 1 -1 -1 -1 -1 -1 -1 0 2 0 2 -1 -1 -1 -1 0 2 0 2 -1 -1 -1 -1 0 2 0 2 1 1 1 -1 -1 -1 -1 0 2 0 2 0 2 0 2 -1 -1 -1 -1 0 2 0 2 -1 -1 -1 -1 1 -1 1 0 2 0 2 -1 -1 -1 -1 -1 -1 -1 -1 0 2 0 2 0 2 0 2 -1 -1 -1 -1 1 1 -1 0 2 0 2 -1 -1 -1 -1 0 2 0 2 -1 -1 -1 -1 -1 -1 -1 -1 0 2 0 2 1 -1 -1 -1 -1 0 2 -1 -1 0 2 0 2 1 -1 0 2 1 -1 1 -1 -1 -1 1 -1 -1 -1 1 1 1 -1 -1 0 2 -1 -1 0 2 1 -1 0 2 1 -1 0 2 -1 -1 1 -1 -1 -1 1 -1 1 -1 1 0 2 -1 -1 0 2 -1 -1 0 2 1 -1 0 2 1 -1 -1 -1 1 -1 -1 -1 1 -1 1 1 -1 0 2 -1 -1 0 2 -1 -1 1 -1 0 2 1 -1 0 2 1 -1 -1 -1 1 -1 -1 -1 1 -1 -1 -1 -1 0 2 0 2 -1 -1 1 -1 -1 -1 -1 -1 1 -1 0 2 1 -1 1 -1 0 2 1 1 1 -1 -1 0 2 0 2 -1 -1 -1 -1 1 -1 1 -1 -1 -1 1 -1 0 2 0 2 1 -1 1 -1 1 0 2 -1 -1 -1 -1 0 2 1 -1 -1 -1 -1 -1 1 -1 1 -1 0 2 0 2 1 -1 1 1 -1 0 2 -1 -1 -1 -1 0 2 -1 -1 1 -1 1 -1 -1 -1 0 2 1 -1 1 -1 0 2 For inital design Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.000096 0.000537 0.000000 Top 6 Left 6 Corner: 0.000333 0.001550 0.000000 Top 7 Left 7 Corner: 0.000006 0.000027 0.000000 Top 8 Left 8 Corner: 0.000000 0.000001 0.000000 Top 9 Left 9 Corner: 0.000001 0.000005 0.000000 Top 10 Left 10 Corner: 0.000000 0.000000 0.000000 Top 11 Left 11 Corner: 0.000000 0.000000 0.000000 Top 12 Left 12 Corner: 0.000000 0.000000 0.000000 Top 13 Left 13 Corner: 0.000005 0.000014 0.000000 Top 14 Left 14 Corner: 0.000012 0.000029 0.000000 Top 15 Left 15 Corner: 0.000263 0.000428 0.000000 Top 16 Left 16 Corner: 0.000457 0.000844 0.000000 Top 17 Left 17 Corner: 0.000679 0.001480 0.000000 Top 18 Left 18 Corner: 0.000966 0.001953 0.000000 Top 19 Left 19 Corner: 0.000254 0.000584 0.000000 Top 20 Left 20 Corner: 0.000365 0.000721 0.000000 Top 21 Left 21 Corner: 0.002705 0.005197 0.000000 Top 22 Left 22 Corner: 0.017886 0.030586 0.000000 Top 23 Left 23 Corner: 0.023719 0.038193 0.000000 Top 24 Left 24 Corner: 0.028538 0.045501 1.000000 Top 25 Left 25 Corner: 0.128907 0.199833 5.432303 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: 0+0i -7.9291e-080-2.563e-080i 0+0i