Optimal maximin $L_{1}$-distance Latin hypercube designs based on good lattice point designs

Abstract

Maximin distance Latin hypercube designs are commonly used for computer experiments, but the construction of such designs is challenging. We construct a series of maximin Latin hypercube designs via Williams transformations of good lattice point designs. Some constructed designs are optimal under the maximin $L_{1}$-distance criterion, while others are asymptotically optimal. Moreover, these designs are also shown to have small pairwise correlations between columns.