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:(a) - f1(x1) f2(x1), ..., f1(xs) f2(xs) Result Design: 1 1 1 2 2 3 2 3 3 1 3 1 1 2 1 2 2 1 2 2 1 3 3 2 3 1 2 1 2 1 2 3 1 2 2 1 2 1 3 2 1 3 2 3 1 2 1 3 2 2 1 2 3 3 3 2 2 1 1 2 3 2 1 1 2 1 1 1 2 2 1 2 3 1 1 2 1 3 3 3 1 1 2 1 3 3 1 1 2 2 2 1 1 2 3 3 1 1 1 1 1 3 3 3 1 3 1 1 1 3 3 1 1 1 1 2 3 1 3 1 1 2 1 2 2 3 2 3 1 2 1 2 1 2 2 1 1 1 2 2 1 2 2 1 2 2 1 2 1 1 1 3 3 2 2 3 1 3 2 2 1 2 2 2 2 2 3 1 3 2 2 1 3 3 1 1 1 2 2 1 3 2 1 3 2 1 3 1 2 3 2 1 1 1 1 2 1 2 1 2 2 3 2 3 3 1 3 1 1 1 1 1 3 2 2 2 3 2 3 3 3 2 2 3 1 2 2 2 3 3 1 2 1 3 3 2 1 1 2 2 2 1 2 2 3 2 2 1 2 3 1 3 1 3 1 2 2 1 1 1 1 1 3 1 2 3 3 1 3 2 2 2 2 2 1 1 1 2 3 3 2 2 3 2 1 1 1 3 1 2 2 1 1 3 2 1 3 2 1 2 3 1 3 2 2 2 2 1 2 1 2 2 2 2 1 1 1 1 2 1 2 2 2 1 1 3 1 1 1 1 3 3 3 3 1 3 2 1 2 2 2 3 2 3 2 3 2 2 3 3 2 3 2 2 1 1 2 3 1 1 3 3 1 3 2 2 2 1 1 2 1 2 2 3 3 2 2 2 3 3 2 3 3 2 2 1 2 2 1 2 1 2 1 2 1 1 2 2 1 2 2 1 2 2 2 1 1 3 1 2 3 2 3 2 3 1 2 2 1 1 3 1 2 2 1 1 2 1 3 3 3 2 1 1 2 1 1 1 2 2 3 3 3 2 2 3 1 1 1 1 1 1 2 1 1 1 2 1 2 2 2 1 1 2 1 2 1 2 3 1 1 3 3 3 1 1 3 1 1 3 1 1 2 1 2 2 3 3 1 1 1 3 3 1 2 2 2 1 1 1 3 3 2 3 1 2 2 3 2 1 1 1 1 2 2 2 1 1 2 3 2 1 1 3 2 2 3 3 2 2 1 2 2 2 2 1 1 3 3 1 2 1 3 3 2 2 2 1 3 2 3 3 3 3 2 2 2 2 3 2 2 1 2 2 3 1 3 1 3 1 3 3 1 1 3 1 Runs Permutation: 5 20 31 10 12 9 13 17 27 22 11 7 29 1 23 8 36 30 19 26 14 4 6 3 28 32 18 21 25 15 33 24 35 34 2 16 Factors Permutation: 1 2 3 4 7 6 14 9 8 10 11 12 15 5 13 16 Max Product Det: 1.7041e-013 ============================================ Expanded Matrix: 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 1 1 -1 -1 1 -1 1 -1 0 2 1 -1 -1 -1 0 2 -1 -1 0 2 -1 -1 0 2 1 -1 1 -1 1 1 -1 0 2 -1 -1 1 -1 0 2 -1 -1 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 0 2 0 2 -1 -1 -1 -1 0 2 1 -1 0 2 -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 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 -1 -1 -1 -1 -1 1 -1 1 -1 1 -1 -1 -1 1 -1 -1 -1 -1 -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 0 2 0 2 -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 -1 -1 1 -1 1 -1 0 2 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 0 2 0 2 -1 -1 1 -1 1 -1 -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 -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 1 -1 0 2 0 2 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 -1 -1 1 -1 1 -1 0 2 -1 -1 -1 -1 0 2 0 2 1 1 -1 1 1 1 -1 0 2 0 2 -1 -1 0 2 1 -1 -1 -1 1 -1 -1 -1 1 -1 -1 -1 0 2 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 0 2 1 1 1 -1 -1 -1 -1 0 2 1 -1 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 1 -1 0 2 -1 -1 1 -1 0 2 -1 -1 0 2 1 -1 -1 -1 1 -1 0 2 1 1 1 1 -1 0 2 -1 -1 0 2 0 2 0 2 0 2 -1 -1 -1 -1 -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 0 2 1 -1 0 2 1 -1 0 2 1 -1 0 2 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 1 -1 -1 -1 1 -1 0 2 0 2 0 2 -1 -1 1 -1 1 -1 1 0 2 1 -1 1 -1 0 2 0 2 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 0 2 -1 -1 0 2 -1 -1 -1 -1 0 2 0 2 -1 -1 0 2 1 1 -1 1 1 0 2 -1 -1 -1 -1 1 -1 -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 0 2 -1 -1 -1 -1 0 2 -1 -1 1 -1 1 -1 1 -1 0 2 1 -1 -1 1 -1 -1 -1 -1 -1 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 0 2 -1 -1 -1 -1 -1 -1 0 2 -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 0 2 0 2 1 -1 1 -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 0 2 1 -1 -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 -1 -1 1 -1 0 2 0 2 1 -1 1 -1 1 1 1 -1 1 0 2 0 2 0 2 -1 -1 -1 -1 1 -1 1 -1 -1 -1 0 2 -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 0 2 0 2 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 Det(X'X)^(1/k) - Std EachStd Original --------------------------- Top 5 Left 5 Corner: 0.130675 0.940863 4.704316 Top 6 Left 6 Corner: 0.136083 0.856599 4.578857 Top 7 Left 7 Corner: 0.171265 0.883390 6.424211 Top 8 Left 8 Corner: 0.191102 0.831625 6.779122 Top 9 Left 9 Corner: 0.203381 0.816074 7.805068 Top 10 Left 10 Corner: 0.234477 0.832466 8.585814 Top 11 Left 11 Corner: 0.226631 0.745990 8.824633 Top 12 Left 12 Corner: 0.242746 0.732165 9.078514 Top 13 Left 13 Corner: 0.266285 0.742446 10.473482 Top 14 Left 14 Corner: 0.275452 0.708799 10.458442 Top 15 Left 15 Corner: 0.293076 0.708645 11.612599 Top 16 Left 16 Corner: 0.337210 0.761151 12.949125 Top 17 Left 17 Corner: 0.325021 0.691361 12.951203 Top 18 Left 18 Corner: 0.355062 0.717479 13.755311 Top 19 Left 19 Corner: 0.377281 0.717646 15.100715 Top 20 Left 20 Corner: 0.395955 0.715733 15.448000 Top 21 Left 21 Corner: 0.424318 0.729004 17.044712 Top 22 Left 22 Corner: 0.462196 0.748566 18.136626 Top 23 Left 23 Corner: 0.483570 0.759286 19.482791 Top 24 Left 24 Corner: 0.503062 0.756585 19.835311 Top 25 Left 25 Corner: 0.529950 0.764986 21.404905 Top 26 Left 26 Corner: 0.542200 0.757016 21.465592 Top 27 Left 27 Corner: 0.576793 0.771189 23.346603 Top 28 Left 28 Corner: 0.609212 0.784386 24.202766 Top 29 Left 29 Corner: 0.634703 0.789124 25.737823 Top 30 Left 29 Corner: 0.696828 0.837206 28.257041 Top 31 Left 29 Corner: 0.743679 0.864701 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: 1.704133776030877e-013 0.0007521042996240538 1.449422708519095e+038 ============================================ Expanded Matrix for initial design: 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 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 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 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 -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 -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 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 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 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 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 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 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 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 -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 -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 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 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 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 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 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 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 -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 -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 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 -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 -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 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 1 -1 0 2 1 -1 0 2 1 -1 -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 -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 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 -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: 0.000000 0.000619 0.000000 Top 6 Left 6 Corner: 0.094355 0.635456 3.174802 Top 7 Left 7 Corner: 0.000880 0.004748 0.000000 Top 8 Left 8 Corner: 0.001610 0.000000 0.000000 Top 9 Left 9 Corner: 0.000078 0.000220 0.000000 Top 10 Left 10 Corner: 0.000156 0.000557 0.000000 Top 11 Left 11 Corner: 0.000012 0.000037 0.000000 Top 12 Left 12 Corner: 0.000002 0.000003 0.000000 Top 13 Left 13 Corner: 0.000004 0.000013 0.000000 Top 14 Left 14 Corner: 0.000012 0.000029 0.000000 Top 15 Left 15 Corner: 0.000250 0.000446 0.000000 Top 16 Left 16 Corner: 0.000410 0.000846 0.000000 Top 17 Left 17 Corner: 0.000758 0.001378 0.000000 Top 18 Left 18 Corner: 0.005670 0.009263 0.000000 Top 19 Left 19 Corner: 0.001295 0.003296 0.000000 Top 20 Left 20 Corner: 0.000300 0.000512 0.000000 Top 21 Left 21 Corner: 0.000496 0.000954 0.000000 Top 22 Left 22 Corner: 0.003704 0.005615 0.000000 Top 23 Left 23 Corner: 0.004344 0.007627 0.000000 Top 24 Left 24 Corner: 0.006145 0.010494 0.000000 Top 25 Left 25 Corner: 0.033171 0.050592 1.256941 Top 26 Left 26 Corner: 0.121622 0.199815 5.418574 Top 27 Left 27 Corner: 0.158300 0.219146 5.819852 Top 28 Left 28 Corner: 0.173924 0.232299 7.223155 Top 29 Left 29 Corner: 0.201703 0.254028 7.882268 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