For a saturated 2^k factorial design, deleting a set of runs preserves unbiased estimation of all non-negligible effects exactly when the corresponding complement matrix is nonsingular, and the D-optimal choice maximizes the determinant of that complement.
Z ivkovi\'c (2006), Classification of small (0 , 1) matrices, Linear Algebra Appl
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The general Nature of Saturated Designs
For a saturated 2^k factorial design, deleting a set of runs preserves unbiased estimation of all non-negligible effects exactly when the corresponding complement matrix is nonsingular, and the D-optimal choice maximizes the determinant of that complement.