Abstract
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 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
Constructions of optimal orthogonal arrays with repeated rows. / Colbourn, Charles; Stinson, Douglas R.; Veitch, Shannon.
In: Discrete Mathematics, Vol. 342, No. 9, 01.09.2019, p. 2455-2466.Research output: Contribution to journal › Article
}
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 -