Constructions of optimal orthogonal arrays with repeated rows

Charles J. Colbourn; Douglas R. Stinson; Shannon Veitch

doi:10.1016/j.disc.2019.05.021

Constructions of optimal orthogonal arrays with repeated rows

Charles J. Colbourn, Douglas R. Stinson, Shannon Veitch

Computing, Informatics and Decision Systems Engineering, School of (CIDSE)

Research output: Contribution to journal › Article › peer-review

Abstract

We construct orthogonal arrays OA_λ(k,n)(of strength two) having a row that is repeated m times, where m is as large as possible. In particular, we consider OAs where the ratio m∕λ is as large as possible; these OAs are termed optimal. We provide constructions of optimal OAs for any k≥n+1, albeit with large λ. We also study basic OAs; these are optimal OAs in which gcd(m,λ)=1. We construct a basic OA with n=2 and k=4t+1, provided that a Hadamard matrix of order 8t+4 exists. This completely solves the problem of constructing basic OAs with n=2, modulo the Hadamard matrix conjecture.

Original language	English (US)
Pages (from-to)	2455-2466
Number of pages	12
Journal	Discrete Mathematics
Volume	342
Issue number	9
DOIs	https://doi.org/10.1016/j.disc.2019.05.021
State	Published - Sep 2019

Keywords

Hadamard matrix
Orthogonal array
Repeated rows

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Access to Document

10.1016/j.disc.2019.05.021

Fingerprint Dive into the research topics of 'Constructions of optimal orthogonal arrays with repeated rows'. Together they form a unique fingerprint.

Cite this

@article{696edf1d8fb94c6f87e824269458962f,

title = "Constructions of optimal orthogonal arrays with repeated rows",

abstract = "We construct orthogonal arrays OAλ(k,n)(of strength two) having a row that is repeated m times, where m is as large as possible. In particular, we consider OAs where the ratio m∕λ is as large as possible; these OAs are termed optimal. We provide constructions of optimal OAs for any k≥n+1, albeit with large λ. We also study basic OAs; these are optimal OAs in which gcd(m,λ)=1. We construct a basic OA with n=2 and k=4t+1, provided that a Hadamard matrix of order 8t+4 exists. This completely solves the problem of constructing basic OAs with n=2, modulo the Hadamard matrix conjecture.",

keywords = "Hadamard matrix, Orthogonal array, Repeated rows",

author = "Colbourn, {Charles J.} and Stinson, {Douglas R.} and Shannon Veitch",

year = "2019",

month = sep,

doi = "10.1016/j.disc.2019.05.021",

language = "English (US)",

volume = "342",

pages = "2455--2466",

journal = "Discrete Mathematics",

issn = "0012-365X",

publisher = "Elsevier",

number = "9",

}

TY - JOUR

T1 - Constructions of optimal orthogonal arrays with repeated rows

AU - Colbourn, Charles J.

AU - Stinson, Douglas R.

AU - Veitch, Shannon

PY - 2019/9

Y1 - 2019/9

N2 - We construct orthogonal arrays OAλ(k,n)(of strength two) having a row that is repeated m times, where m is as large as possible. In particular, we consider OAs where the ratio m∕λ is as large as possible; these OAs are termed optimal. We provide constructions of optimal OAs for any k≥n+1, albeit with large λ. We also study basic OAs; these are optimal OAs in which gcd(m,λ)=1. We construct a basic OA with n=2 and k=4t+1, provided that a Hadamard matrix of order 8t+4 exists. This completely solves the problem of constructing basic OAs with n=2, modulo the Hadamard matrix conjecture.

AB - We construct orthogonal arrays OAλ(k,n)(of strength two) having a row that is repeated m times, where m is as large as possible. In particular, we consider OAs where the ratio m∕λ is as large as possible; these OAs are termed optimal. We provide constructions of optimal OAs for any k≥n+1, albeit with large λ. We also study basic OAs; these are optimal OAs in which gcd(m,λ)=1. We construct a basic OA with n=2 and k=4t+1, provided that a Hadamard matrix of order 8t+4 exists. This completely solves the problem of constructing basic OAs with n=2, modulo the Hadamard matrix conjecture.

KW - Hadamard matrix

KW - Orthogonal array

KW - Repeated rows

UR - http://www.scopus.com/inward/record.url?scp=85066617377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066617377&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2019.05.021

DO - 10.1016/j.disc.2019.05.021

M3 - Article

AN - SCOPUS:85066617377

VL - 342

SP - 2455

EP - 2466

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 9

ER -