Efficient Nearly Orthogonal and Space-Filling Latin Hypercubes

This article presents an algorithm for constructing orthogonal Latin hypercubes, given a fixed sample size, in more dimensions than previous approaches. In addition, we detail a method that dramatically improves the space-filling properties of the resultant Latin hypercubes at the expense of inducing small correlations between the columns in the design matrix. Although the designs are applicable to many situations, they were developed to provide Department of Defense analysts flexibility in fitting models when exploring high-dimensional computer simulations where there is considerable a priori uncertainty about the forms of the response surfaces.