On maximin distance and nearly orthogonal Latin hypercube designs

Maximin distance Latin hypercube designs (LHDs) are frequently used in computer experiments, but their constructions are challenging. In this paper, we present some new results connecting maximin L₂-distance optimality and near orthogonality for mirror-symmetric LHDs. We further propose a simple and effective method for constructing nearly orthogonal LHDs that can yield almost the largest minimum distance. The obtained designs with small and medium sizes are tabulated and their superior performances are illustrated via comparisons.