{"title":"New results on asymmetric orthogonal arrays with strength t ≥ 3","authors":"","doi":"10.1016/j.disc.2024.114264","DOIUrl":null,"url":null,"abstract":"<div><p>The orthogonal array holds significant importance as a research topic within the realms of combinatorial design theory and experimental design theory, with widespread applications in statistics, computer science, coding theory and cryptography. This paper presents three constructions for asymmetric orthogonal arrays including juxtaposition, generator matrices over Galois fields and mixed difference matrices. Subsequently, many new infinite families of asymmetric orthogonal arrays with strength <span><math><mi>t</mi><mo>≥</mo><mn>3</mn></math></span> are obtained. Furthermore, some new infinite families of large sets of orthogonal arrays with mixed levels are also obtained.</p></div>","PeriodicalId":50572,"journal":{"name":"Discrete Mathematics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2024-09-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Discrete Mathematics","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0012365X24003959","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
The orthogonal array holds significant importance as a research topic within the realms of combinatorial design theory and experimental design theory, with widespread applications in statistics, computer science, coding theory and cryptography. This paper presents three constructions for asymmetric orthogonal arrays including juxtaposition, generator matrices over Galois fields and mixed difference matrices. Subsequently, many new infinite families of asymmetric orthogonal arrays with strength are obtained. Furthermore, some new infinite families of large sets of orthogonal arrays with mixed levels are also obtained.
期刊介绍：
Discrete Mathematics provides a common forum for significant research in many areas of discrete mathematics and combinatorics. Among the fields covered by Discrete Mathematics are graph and hypergraph theory, enumeration, coding theory, block designs, the combinatorics of partially ordered sets, extremal set theory, matroid theory, algebraic combinatorics, discrete geometry, matrices, and discrete probability theory.
Items in the journal include research articles (Contributions or Notes, depending on length) and survey/expository articles (Perspectives). Efforts are made to process the submission of Notes (short articles) quickly. The Perspectives section features expository articles accessible to a broad audience that cast new light or present unifying points of view on well-known or insufficiently-known topics.
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