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On maximin distance and nearly orthogonal Latin hypercube designs. (English) Zbl 1455.62151

Summary: 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 \(L_2\)-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.

MSC:

62K10 Statistical block designs
62K15 Factorial statistical designs
62-08 Computational methods for problems pertaining to statistics
05B15 Orthogonal arrays, Latin squares, Room squares
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