Elsevier

Discrete Mathematics

Volume 342, Issue 9, September 2019, Pages 2455-2466
Discrete Mathematics

Constructions of optimal orthogonal arrays with repeated rows

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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 mλ is as large as possible; these OAs are termed optimal. We provide constructions of optimal OAs for any kn+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

Orthogonal array
Repeated rows
Hadamard matrix

Cited by (0)

1

C.J. Colbourn’s research is supported by the U.S. National Science Foundation grant #1813729..

2

D.R. Stinson’s research is supported by NSERC discovery grant RGPIN-03882..