On Design Orthogonality, Maximin Distance, and Projection Uniformity for Computer Experiments

Space-filling designs are widely used in both computer and physical experiments. Column-orthogonality, maximin distance, and projection uniformity are three basic and popular space-filling criteria proposed from different perspectives, but their relationships have been rarely investigated. We show that the average squared correlation metric is a function of the pairwise L ₂-distances between the rows only. We further explore the connection between uniform projection designs and maximin L ₁-distance designs. Based on these connections, we develop new lower and upper bounds for column-orthogonality and projection uniformity from the perspective of distance between design points. These results not only provide new theoretical justifications for each criterion but also help in finding better space-filling designs under multiple criteria. Supplementary materials for this article are available online.