Schur- and E-optimal two-level factorial designs

Schur-optimality is a very general class of optimality criteria that includes, as special cases, A- D- and E-optimality and Cheng Type 1 optimality. In this paper, Schur-optimal two-level factorial designs under a second-order model are derived for 3 and 5 factors for all numbers of runs where the model is estimable. In addition, orthogonal arrays of strength 4 (resolution V) with e added runs are shown to be E-optimal under a second-order model for e⩽10 and m=4 factors and for e⩽15 and m⩾5 factors. Corresponding results for third-order models are also given.