Strong orthogonal arrays of strength 2+ with better two-dimensional projection properties

Space-filling properties are favored in designs of computer experiments. Strong orthogonal arrays of strength 2+ are a class of space-filling designs that guarantee 4 by 2 and 2 by 4 two-dimensional space-filling properties. However, the patterns of the two-dimensional projections can be very different with some being notably better than the others. In a strong orthogonal array of strength 2+, we would like to have more of better patterns among the two factor projections. The objective of this study is to identify strong orthogonal arrays of strength 2+ with better two-dimensional projection properties, utilizing two selection criteria. We use second order saturated designs to construct strong orthogonal arrays of strength 2+ and evaluate all available second order saturated designs to find good designs with 16 runs. Designs are identified for the number of factors, m = 6, 7, 8, 9, and 10, according to both selection criteria. The study is extended to 32 runs, using 3 out of 12 second order saturated designs to identify designs with better two-dimensional projection properties for m = 10 to 21 under both selection criteria.