A new class of asymptotic maximin distance Latin hypercube designs

Abstract Maximin distance Latin hypercube designs have been widely used in computer experiments because they can achieve one‐dimensional stratification and full‐dimensional space‐filling properties. In this article, we propose a new method for constructing a class of Latin hypercube designs that can accommodate many columns. We show that the resulting designs are asymptotically optimal under the maximin distance criterion, and enjoy a large proportion of low‐dimensional stratification properties that strong orthogonal arrays should have. In addition, the proposed method can be used to construct a class of asymptotically optimal sliced maximin distance Latin hypercube designs. These designs are well suited to computer experiments due to their good space‐filling properties.