Polynomial regression in $q$ variables of degree $n$ on the $q$-cube is considered. Approximate $D$-optimal and approximate $D_s$-optimal designs for estimating higher degree terms are investigated. Numerical results are given for $n = 2$ with arbitrary $q$ and for $n = 3, 4, 5$ and $q = 2, 3$. Exact solutions are given within the class of product designs together with some efficiency calculations.
"Efficient $D_s$-Optimal Designs for Multivariate Polynomial Regression on the $q$-Cube." Ann. Statist. 16 (3) 1225 - 1240, September, 1988. https://doi.org/10.1214/aos/1176350957