Construction of orthogonal arrays of strength three by augmented difference schemes

被引：13

作者：

Zhang, Xiao ^{[1
]}

Pang, Shanqi ^{[1
]}

Chen, Guangzhou ^{[1
]}

机构：

[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Peoples R China

来源：

DISCRETE MATHEMATICS | 2022年 / 345卷 / 11期

基金：

中国国家自然科学基金;

关键词：

Augmented difference scheme; Difference scheme; Galois field; Orthogonal array; Strength three; ENUMERATION; EXISTENCE;

D O I：

10.1016/j.disc.2022.113041

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Difference schemes are a powerful tool for developing orthogonal arrays (OAs). In this study, we define an augmented difference scheme, i.e., a generalization of a difference scheme, and present a general method for constructing such schemes of strength three. As an application of the proposed method, we construct difference schemes with any number of levels, including D3(d2, c, d) with the maximal value c for any prime power d. Furthermore, using the newly constructed difference schemes, a large number of new OAs of strength three can be infinitely obtained, including many tight arrays. Accordingly, we provide a positive answer to two open problems: how to develop new methods for the construction of difference schemes of high strength with the ultimate goal of obtaining better OAs of high strength, and how to develop better methods and tools for the construction of OAs.

引用

页数：12