TA Algorithm to find a lean design
Runs n=9, Factors s=4.
Initial Design:
 1 3 1 2
 1 2 3 3
 3 2 1 1
 2 2 2 2
 2 1 1 3
 2 3 3 1
 1 1 2 1
 3 1 3 2
 3 3 2 3
Criterion: maximize Det(X(5)'X(5))*...*Det(X(9)'X(9))
Search Type:(b) - f1(x1) ... f1(xs) f2(x1) ... f2(xs)
Result Design:
 1 3 1 2
 1 2 3 3
 3 2 1 1
 1 1 2 1
 2 1 1 3
 2 3 3 1
 3 3 2 3
 3 1 3 2
 2 2 2 2

Runs Permutation: 1  2  3  7  5  6  9  8  4
Factors Permutation: 1  2  3  4

Max Product Det: 0.18262
============================================
Expanded Matrix:
  1 -1  1 -1  0 -1 -1 -1  2
  1 -1  0  1  1 -1  2 -1 -1
  1  1  0 -1 -1 -1  2 -1 -1
  1 -1 -1  0 -1 -1 -1  2 -1
  1  0 -1 -1  1  2 -1 -1 -1
  1  0  1  1 -1  2 -1 -1 -1
  1  1  1  0  1 -1 -1  2 -1
  1  1 -1  1  0 -1 -1 -1  2
  1  0  0  0  0  2  2  2  2
Det(X'X)^(1/k) -         Std    EachStd   Original
                        ---------------------------
Top  5 Left  5 Corner: 0.488359 0.804738 3.177672
Top  6 Left  6 Corner: 0.617715 0.860153 4.762203
Top  7 Left  7 Corner: 0.730600 0.898641 6.357804
Top  8 Left  8 Corner: 0.828607 0.923999 7.896444
Top  9 Left  9 Corner: 1.000000 1.000000 10.227532
   Det Product: 0.18262301     0.57476267      7770.0975
============================================
Expanded Matrix for initial design:
  1 -1  1 -1  0 -1 -1 -1  2
  1 -1  0  1  1 -1  2 -1 -1
  1  1  0 -1 -1 -1  2 -1 -1
  1  0  0  0  0  2  2  2  2
  1  0 -1 -1  1  2 -1 -1 -1
  1  0  1  1 -1  2 -1 -1 -1
  1 -1 -1  0 -1 -1 -1  2 -1
  1  1 -1  1  0 -1 -1 -1  2
  1  1  1  0  1 -1 -1  2 -1
For inital design
Det(X'X)^(1/k) -         Std    EachStd   Original
                        ---------------------------
Top  5 Left  5 Corner: 0.000222 0.000444 0.000000
Top  6 Left  6 Corner: 0.001045 0.001680 0.000000
Top  7 Left  7 Corner: 0.599337 0.759999 5.215532
Top  8 Left  8 Corner: 0.696772 0.792550 6.640092
Top  9 Left  9 Corner: 1.000000 1.000000 10.227532
   Det Product: 5.6132e-008+1.2607e-007i 2.6101e-007+5.8623e-007i           0+0i