Musings about Constructions of Efficient Latin Hypercube Designs with Flexible Run-sizes

Abstract: Efficient Latin hypercube designs (LHDs), including maximin distance LHDs, maximum projection LHDs and orthogonal LHDs, are widely used in computer experiments. It is challenging to construct such designs with flexible sizes, especially for large ones. In the current literature, various algebraic methods and search algorithms have been proposed for identifying efficient LHDs, each having its own pros and cons. In this paper, we review, summarize and compare some currently popular methods aiming to provide guidance for experimenters on what method should be used in practice. Using the R package we developed which integrates and improves various algebraic and searching methods, many of the designs found in this paper are better than the existing ones. They are easy to use for practitioners and can serve as benchmarks for the future developments on LHDs.