### 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 | |

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

*Discrete Mathematics*,

*342*(9), 2455-2466. https://doi.org/10.1016/j.disc.2019.05.021

**Constructions of optimal orthogonal arrays with repeated rows.** / Colbourn, Charles; Stinson, Douglas R.; Veitch, Shannon.

Research output: Contribution to journal › Article

*Discrete Mathematics*, vol. 342, no. 9, pp. 2455-2466. https://doi.org/10.1016/j.disc.2019.05.021

}

TY - JOUR

T1 - Constructions of optimal orthogonal arrays with repeated rows

AU - Colbourn, Charles

AU - Stinson, Douglas R.

AU - Veitch, Shannon

PY - 2019/9/1

Y1 - 2019/9/1

N2 - 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.

AB - 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.

KW - Hadamard matrix

KW - Orthogonal array

KW - Repeated rows

UR - http://www.scopus.com/inward/record.url?scp=85066617377&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85066617377&partnerID=8YFLogxK

U2 - 10.1016/j.disc.2019.05.021

DO - 10.1016/j.disc.2019.05.021

M3 - Article

VL - 342

SP - 2455

EP - 2466

JO - Discrete Mathematics

JF - Discrete Mathematics

SN - 0012-365X

IS - 9

ER -