TY - JOUR

T1 - Constructions of optimal orthogonal arrays with repeated rows

AU - Colbourn, Charles J.

AU - Stinson, Douglas R.

AU - Veitch, Shannon

N1 - Funding Information:
C.J. Colbourn's research is supported by the U.S. National Science Foundation grant #1813729.D.R. Stinson's research is supported by NSERC discovery grant RGPIN-03882. This work benefitted from the use of the CrySP RIPPLE Facility at the University of Waterloo. Also, we would like to thank Sophie Toulouse for bringing this problem to our attention. The authors declare that they have no conflict of interest.
Publisher Copyright:
© 2019 Elsevier B.V.

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 -