I have a design matrix with 18 runs. A and B are three-level categorical variables (low, mid , high and small, medium and large), and C is a two-level categorical variable (male, female). Here's an example
| runs | low | mid | small | medium | male |
|--------|-----|-----|-------|--------|------|
| run 1 | 1 | -1 | 1 | -1 | 1 |
| run 2 | 1 | -1 | 1 | -1 | -1 |
| run 3 | 1 | -1 | -1 | 1 | 1 |
| run 4 | 1 | -1 | -1 | 1 | -1 |
| run 5 | 1 | -1 | -1 | -1 | 1 |
| run 6 | 1 | -1 | -1 | -1 | -1 |
| run 7 | -1 | 1 | 1 | -1 | 1 |
| run 8 | -1 | 1 | 1 | -1 | -1 |
| run 9 | -1 | 1 | -1 | 1 | 1 |
| run 10 | -1 | 1 | -1 | 1 | -1 |
| run 11 | -1 | 1 | -1 | -1 | 1 |
| run 12 | -1 | 1 | -1 | -1 | -1 |
| run 13 | -1 | -1 | 1 | -1 | 1 |
| run 14 | -1 | -1 | 1 | -1 | -1 |
| run 15 | -1 | -1 | -1 | 1 | 1 |
| run 16 | -1 | -1 | -1 | 1 | -1 |
| run 17 | -1 | -1 | -1 | -1 | 1 |
| run 18 | -1 | -1 | -1 | -1 | -1 |
Is it possible to select runs for a fractional design based on this matrix or is there an algorithm that would allow me to do it for more complex setups?