康佐航, 欧祖军, 李洪毅, 刘旭. Triple设计的空间填充性质[J]. 应用概率统计, 2025, 41(6): 822-836. DOI: 10.12460/j.issn.1001-4268.aps.2025.2024032
引用本文: 康佐航, 欧祖军, 李洪毅, 刘旭. Triple设计的空间填充性质[J]. 应用概率统计, 2025, 41(6): 822-836. DOI: 10.12460/j.issn.1001-4268.aps.2025.2024032
KANG Zuohang, OU Zujun, LI Hongyi, LIU Xu, . Space-Filling Properties of Triple Designs[J]. Chinese Journal of Applied Probability and Statistics, 2025, 41(6): 822-836.
Citation: KANG Zuohang, OU Zujun, LI Hongyi, LIU Xu, . Space-Filling Properties of Triple Designs[J]. Chinese Journal of Applied Probability and Statistics, 2025, 41(6): 822-836.

Triple设计的空间填充性质

Space-Filling Properties of Triple Designs

  • 摘要: 倍扩方法常用于构造性质优良的大型设计. 本文基于Triple设计的倍扩结构在最大最小L_2-距离准则下讨论了其空间填充性质, 获得了Triple设计的最大最小L_2-距离上界. 基于字长计数器得到了Triple设计广义字长型的快速计算方式, 并获得了Triple设计的字长计数器下界. 数值例子表明Triple设计具有良好的空间填充性, 且能够达到最大最小L_2-距离上界和字长计数器下界.

     

    Abstract: The amplified method is commonly used to construct large-scale designs with excellent properties. In this paper, the space-filling properties of Triple designs with amplified structure are discussed under the maximin L_2-distance criterion, and an upper bound on the maximin L_2-distance of Triple designs is obtained. A fast computation method of the generalized wordlength pattern of the Triple design is obtained based on the wordlength enumerator, and a lower bound on the wordlength enumerator of the Triple design is obtained. Numerical examples show that the Triple designs have good space-filling properties, both the upper bound of the maximin L_2-distance and lower bound of wordlength enumerator are attainable.

     

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