Abstract

Space-filling Latin hypercube designs have found widespread applications in com

puter experiments, yet the construction methods for such designs pose significant challenges.

Algebraic methods are only applicable to a very limited number of runs and factors, while

algorithmic searches often struggle with computational feasibility for large designs, especially

when there is a need to maintain the statistical efficiency above a certain level. To address

these limitations, an approach is proposed for producing space-filling Latin hypercube designs

that can accommodate flexible numbers of runs and factors. The proposed approach is hybrid

in nature, incorporating an algebraic method and its corresponding algorithm. The algebraic

method, built on good lattice point sets and level permutation techniques, applies to any run

size and flexible numbers of factors. The proposed algorithmic search can further accommodate

any number of factors, especially those not covered by the algebraic method. A theoretical

analysis of optimality is provided for the algebraic component. Numerical studies demonstrate

the superior Lp-distance properties of the proposed designs. Furthermore, it is shown that the

proposed designs exhibit good column-orthogonality and projection uniformity as well.

Information

Preprint No.SS-2024-0145
Manuscript IDSS-2024-0145
Complete AuthorsXueru Zhang, Dennis K.J. Lin, Wei Zheng
Corresponding AuthorsWei Zheng
Emailswzheng9@utk.edu

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Acknowledgments

Zhang was supported by Fundamental Research Funds for the Central Universities

Grant FRF-TP-25-044. Lin was supported by National Science Foundation via Grant

Supplementary Materials

The online Supplementary Material includes detailed proofs, algorithms based on

the leave-one-out additive column expansion, quantitative comparisons between the

proposed method and existing methods based on criteria such as the Lp-distance,

column-orthogonality, projection uniformity and computational costs.

Supplementary materials are available for download.