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Space-filling properties of good lattice point sets

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  • Yongdao Zhou
  • Hongquan Xu

Abstract

We study space-filling properties of good lattice point sets and obtain some general theoretical results. We show that linear level permutation does not decrease the minimum distance for good lattice point sets, and we identify several classes of such sets with large minimum distance. Based on good lattice point sets, some maximin distance designs are also constructed.

Suggested Citation

  • Yongdao Zhou & Hongquan Xu, 2015. "Space-filling properties of good lattice point sets," Biometrika, Biometrika Trust, vol. 102(4), pages 959-966.
    • Handle: RePEc:oup:biomet:v:102:y:2015:i:4:p:959-966.
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    File URL: http://hdl.handle.net/10.1093/biomet/asv044
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    Cited by:

    1. Poonam Singh & Himanshu Shukla, 2023. "Uniform mixture designs using designs in 2-dimensional spherical region," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 14(5), pages 1888-1897, October.
    2. 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.
    3. Su, Zheren & Wang, Yaping & Zhou, Yingchun, 2020. "On maximin distance and nearly orthogonal Latin hypercube designs," Statistics & Probability Letters, Elsevier, vol. 166(C).
    4. 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.
    5. Wang, Chunyan & Lin, Dennis K.J., 2024. "Strong orthogonal Latin hypercubes for computer experiments," Computational Statistics & Data Analysis, Elsevier, vol. 198(C).
    6. Zong-Feng Qi & Xue-Ru Zhang & Yong-Dao Zhou, 2018. "Generalized good lattice point sets," Computational Statistics, Springer, vol. 33(2), pages 887-901, June.
    7. Qiming Bai & Hongyi Li & Xingyou Huang & Huili Xue, 2023. "Design efficiency for minimum projection uniform designs with q levels," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 86(5), pages 577-594, July.
    8. Tonghui Pang & Yan Wang & Jian-Feng Yang, 2022. "Asymptotically optimal maximin distance Latin hypercube designs," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 85(4), pages 405-418, May.

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