TY - JOUR

T1 - Constructions of optimal orthogonal arrays with repeated rows

AU - Colbourn, Charles J.

AU - Stinson, Douglas R.

AU - Veitch, Shannon

N1 - Publisher Copyright:
© 2019 Elsevier B.V.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.

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 -