D-optimal saturated designs for main effects and interactions in 2 k -factorial experiments

In a 2k-factorial experiment with limited resources, when practitioners can identify the non-negligible effects and interactions beforehand, it is common to run an experiment with a saturated design that ensures the unbiased estimation of the non-negligible parameters of interest. We propose a method for the construction of D-optimal saturated designs for the mean, the main effects, and the second-order interactions of one factor with the remaining factors. In the process, we show the problem is just as hard as the Hadamard determinant problem.