Abstract

Computer experiments have been widely used to build high-quality surrogate models

for complex emulation systems.

Orthogonal Latin hypercubes are efficient designs for computer experiments as they enjoy both orthogonality and one-dimensional maximum stratifi-

cation. Mirror-symmetric designs have also been advocated for computer experiments. The

mirror-symmetry structure can yield higher-order orthogonality and significantly benefit the

identification of the main and interaction effects. The construction of mirror-symmetric orthogonal Latin hypercubes is limited and challenging. This paper proposes a construction method

for mirror-symmetric orthogonal Latin hypercubes using orthogonal arrays from Reed-Solomon

codes. Theoretical results guarantee that the resulting designs enjoy attractive orthogonality and low-dimensional space-filling properties. Moreover, some of the resulting designs are

optimal under the maximin distance criterion. Simulation comparisons are also provided to

demonstrate the superiority of the proposed designs over existing designs.

Information

Preprint No.SS-2025-0049
Manuscript IDSS-2025-0049
Complete AuthorsChunyan Wang, Min-Qian Liu
Corresponding AuthorsMin-Qian Liu
Emailsmqliu@nankai.edu.cn

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Acknowledgments

The authors thank Editor Judy Huixia Wang, an associate editor, and two referees for their valuable comments and suggestions. This work was supported by the

National Natural Science Foundation of China (Grant Nos. 12301323, 12131001 and

12371260), the MOE Project of Key Research Institute of Humanities and Social Sciences (22JJD110001), and Tianjin Science and Technology Program (24ZXZSSS00320).

Wang is affiliated with the Center for Applied Statistics and the School of Statistics at

Renmin University of China. Liu is affiliated with the NITFID, LPMC, KLMDASR,

and the School of Statistics and Data Science at Nankai University.

Supplementary Materials

The online Supplementary Material includes the proofs of Theorems 1–5 and Propositions 1–2, as well as three tables, where Tables S.1, S.2, and S.3 list the invariant

OA(81, 9, 9, 2), mirror-symmetric OA(9, 4, 3, 2), and MSOLH(81, 32) in Example 2, respectively.

Supplementary materials are available for download.