具有重复行的强度 2 的最优正交表的构造

具有重复行的强度 2 的最优正交表的构造

The Construction of Optimal Orthogonal Arrays with Repeated Rows and Strength 2

摘要/Abstract

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数学物理学报 ›› 2025, Vol. 45 ›› Issue (2): 584-603.

庞善起^*(),路又维(),王静()

河南师范大学数学与统计学院河南新乡 453007

收稿日期:2024-06-18 修回日期:2024-09-24 出版日期:2025-04-26 发布日期:2025-04-09
通讯作者: 庞善起 E-mail:pangshanqi@263.net;1277686343@qq.com;wangjing19@126.com
作者简介:路又维，E-mail: 1277686343@qq.com;|王静，E-mail: wangjing19@126.com
基金资助:
国家自然科学基金(11971004);国家自然科学基金(12201189);国家自然科学基金(12471245);中国博士后科学基金(2022M721055);河南省自然科学基金(242300421164)

Shanqi Pang^*(),Youwei Lu(),Jing Wang()

School of Mathematics and Statistics, Henan Normal University, Henan Xinxiang 453007

Received:2024-06-18 Revised:2024-09-24 Online:2025-04-26 Published:2025-04-09
Contact: Shanqi Pang E-mail:pangshanqi@263.net;1277686343@qq.com;wangjing19@126.com
Supported by:
NSFC(11971004);NSFC(12201189);NSFC(12471245);CPSF(2022M721055);Natural Science Foundation of Henan(242300421164)

摘要：

具有重复行的正交表已经得到广泛应用, 它可以降低试验的复杂性和成本, 同时提高试验结果的可靠性. 具有重复行的最优正交表有更好的统计性质和组合结构, 然而目前对此类的最优正交表知之甚少. 该文主要研究各种水平变换和列变换构造具有重复行的最优正交表的方法. 首先介绍了一种独立列构造饱和的正交表的方法, 然后利用各种水平变换和列变换提出了具有重复行的最优正交表和 $m$ -最优正交表的构造方法, 最后作为这些方法的应用为使用人员提供了具有重复行的最优正交表的无穷类.

关键词: 正交表, 具有重复行的正交表, 具有重复行的最优正交表, 水平变换和列变换

Abstract:

Orthogonal arrays with repeated rows have been widely used, which can reduce the complexity and cost of experiments and improve the reliability of experimental results. The optimal orthogonal arrays with repeated rows has better statistical properties and combinatorial structure, but little is known about this kind of optimal orthogonal arrays. In this paper, we mainly study the methods of constructing the optimal orthogonal arrays with repeated rows by various permutation of levels and permutation of columns. Firstly, a method of constructing saturated orthogonal arrays by using independent columns is introduced. Then, the construction methods of optimal orthogonal arrays with repeated rows and $m$ -optimal orthogonal arrays are proposed by using various permutation of levels or columns. Finally, several infinite class of optimal orthogonal arrays with repeated rows are obtained and provided for users.

Key words: orthogonal array, orthogonal array with repeated rows, optimal orthogonal array with repeated rows, permutation of levels and permutation of columns

中图分类号:

O212.6

庞善起,路又维,王静. 具有重复行的强度 2 的最优正交表的构造[J]. 数学物理学报, 2025, 45(2): 584-603.

Shanqi Pang,Youwei Lu,Jing Wang. The Construction of Optimal Orthogonal Arrays with Repeated Rows and Strength 2[J]. Acta mathematica scientia,Series A, 2025, 45(2): 584-603.

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