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Construction of maximin distance Latin squares and related Latin hypercube designs

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  • Qian Xiao
  • Hongquan Xu

Abstract

SummaryMaximin distance Latin hypercube designs are widely used in computer experiments, yet their construction is challenging. Based on number theory and finite fields, we propose three algebraic methods to construct maximin distance Latin squares as special Latin hypercube designs. We develop lower bounds on their minimum distances. The resulting Latin squares and related Latin hypercube designs have larger minimum distances than existing ones, and are especially appealing for high-dimensional applications.

Suggested Citation

  • Qian Xiao & Hongquan Xu, 2017. "Construction of maximin distance Latin squares and related Latin hypercube designs," Biometrika, Biometrika Trust, vol. 104(2), pages 455-464.
    • Handle: RePEc:oup:biomet:v:104:y:2017:i:2:p:455-464.
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    File URL: http://hdl.handle.net/10.1093/biomet/asx006
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    References listed on IDEAS

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    1. Kleijnen, J.P.C., 1997. "Sensitivity analysis and related analyses : A review of some statistical techniques," Other publications TiSEM 7969b135-47c5-4d76-9241-c, Tilburg University, School of Economics and Management.
    2. Yongdao Zhou & Hongquan Xu, 2015. "Space-filling properties of good lattice point sets," Biometrika, Biometrika Trust, vol. 102(4), pages 959-966.
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    Cited by:

    1. Liuqing Yang & Yongdao Zhou & Min-Qian Liu, 2021. "Maximin distance designs based on densest packings," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 84(5), pages 615-634, July.
    2. Su, Zheren & Wang, Yaping & Zhou, Yingchun, 2020. "On maximin distance and nearly orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 166(C).
    3. Yuxin Sun & Wenjun Liu & Ye Tian, 2024. "Projection-Uniform Subsampling Methods for Big Data," Mathematics, MDPI, vol. 12(19), pages 1-16, September.
    4. Wang, Chunyan & Lin, Dennis K.J., 2024. "Strong orthogonal Latin hypercubes for computer experiments," Computational Statistics & Data Analysis, Elsevier, vol. 198(C).

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