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

作　　者：庞善起[1] 路又维 王静[1] Pang Shanqi;Lu Youwei;Wang Jing(School of Mathematics and Statistics,Henan Normal University,Henan Xinciang 453007)

机构地区：[1]河南师范大学数学与统计学院,河南新乡453007

出　　处：《数学物理学报(A辑)》2025年第2期584-603,共20页Acta Mathematica Scientia

基　　金：国家自然科学基金(11971004,12201189,12471245);中国博士后科学基金(2022M721055);河南省自然科学基金(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.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.

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 

分 类 号：O212.6[理学—概率论与数理统计]