Design selection for strong orthogonal arrays

Strong orthogonal arrays (SOAs) were recently introduced and studied as a class of space-filling designs for computer experiments. An important problem that has not been addressed in the literature is that of design selection for such arrays. In this article, we conduct a systematic investigation into this problem, and we focus on the most useful SOA(n,m,4,2 +)s and SOA(n,m,4,2)s. This article first addresses the problem of design selection for SOAs of strength 2+ by examining their three-dimensional projections. Both theoretical and computational results are presented. When SOAs of strength 2+ do not exist, we formulate a general framework for the selection of SOAs of strength 2 by looking at their two-dimensional projections. The approach is fruitful, as it is applicable when SOAs of strength 2+ do not exist and it gives rise to them when they do.