Efficient lack of fit designs that are optimal to estimate the highest coefficient of a polynomial

To solve this problem, efficient lack of fit designs were introduced in Bischoff and Miller [2003. Optimal designs efficient for lack of fit tests. Preprint.]. In this class of designs we explicitly determine ek-optimal designs for polynomial regression of degree k-1 in this paper. More exactly, for k⩽4 we determine all ek-optimal designs for polynomial regression of degree k-1. For k>4 we determine the ek-optimal designs for polynomial regression of degree k-1 if we restrict ourselves to designs that deliver highly efficient lack of fit tests.