Construction of Column-Orthogonal Designs with Two-Dimensional Stratifications

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For the design of computer experiments, column orthogonality and space-filling are two desirable properties. In this paper, we develop methods for constructing a new class of column-orthogonal designs (ODs) with two-dimensional stratifications on finer grids, including orthogonal Latin hypercube designs (OLHDs) as special cases. In addition to being column-orthogonal, these designs have good space-filling properties in two dimensions. The resulting designs achieve stratifications on s2×s or s×s2 grids, and most column pairs satisfy stratifications on s2×s2 grids. Moreover, many column pairs can achieve stratifications on s4×s2 and s2×s4 grids. Furthermore, the obtained space-filling ODs can have s6 levels, s4 levels, and mixed levels, as required for different needs.