A new class of asymptotic maximin distance Latin hypercube designs

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.