Uniform Projection Designs and Strong Orthogonal Arrays
研究了均匀投影设计与强度2+强正交数组之间的联系，发现强正交数组在均匀投影准则下是最优或接近最优的，适合用于计算机实验和二维边际空间填充。
We explore the connections between uniform projection designs and strong orthogonal arrays of strength 2+ in this article. Both of these classes of designs are suitable designs for computer experiments and space-filling in two-dimensional margins, but they are motivated by different considerations. Uniform projection designs are introduced by Sun, Wang, and Xu to capture two-dimensional uniformity using the centered L2-discrepancy whereas strong orthogonal arrays of strength 2+ are brought forth by He, Cheng, and Tang as they achieve stratifications in two-dimensions on finer grids than ordinary orthogonal arrays. We first derive a new expression for the centered L2-discrepancy, which gives a decomposition of the criterion into a sum of squares where each square measures one aspect of design uniformity. This result is not only insightful in itself but also allows us to study strong orthogonal arrays in terms of the discrepancy criterion. More specifically, we show that strong orthogonal arrays of strength 2+ are optimal or nearly optimal under the uniform projection criterion.