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arXiv · 1812.05147

Constructions of optimal orthogonal arrays with repeated rows

Charles J. Colbourn·Douglas R. Stinson·Shannon Veitch
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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 $k \geq n+1$, 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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Charles J. Colbourn, Douglas R. Stinson, Shannon Veitch. 2018-12-12. Constructions of optimal orthogonal arrays with repeated rows. https://arxiv.org/abs/1812.05147

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