Constructions of optimal orthogonal arrays with repeated rows

Charles J. Colbourn, Douglas R. Stinson, Shannon Veitch

Research output: Contribution to journalArticlepeer-review

1 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)2455-2466
Number of pages12
JournalDiscrete Mathematics
Issue number9
StatePublished - Sep 2019


  • Hadamard matrix
  • Orthogonal array
  • Repeated rows

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics


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