Constructions of optimal orthogonal arrays with repeated rows

Charles Colbourn; Douglas R. Stinson; Shannon Veitch

doi:10.1016/j.disc.2019.05.021

Constructions of optimal orthogonal arrays with repeated rows

Charles Colbourn, Douglas R. Stinson, Shannon Veitch

Engineering, Ira A. Fulton Schools of (IAFSE)

Research output: Contribution to journal › Article

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 with n=2, modulo the Hadamard matrix conjecture.

Original language	English (US)
Pages (from-to)	2455-2466
Number of pages	12
Journal	Discrete Mathematics
Volume	342
Issue number	9
DOIs	https://doi.org/10.1016/j.disc.2019.05.021
State	Published - Sep 1 2019

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Keywords

Hadamard matrix
Orthogonal array
Repeated rows

ASJC Scopus subject areas

Theoretical Computer Science
Discrete Mathematics and Combinatorics

Cite this

Colbourn, C., Stinson, D. R., & Veitch, S. (2019). Constructions of optimal orthogonal arrays with repeated rows. Discrete Mathematics, 342(9), 2455-2466. https://doi.org/10.1016/j.disc.2019.05.021

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10.1016/j.disc.2019.05.021