Constructions of optimal orthogonal arrays with repeated rows

2018/12/12 by Colbourn, Charles J., Stinson, Douglas R., Veitch, Shannon · 1 citation
#05B15 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1812.05147

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 wth n=2, modulo the Hadamard matrix conjecture.

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