TY - JOUR
T1 - Constructions of optimal orthogonal arrays with repeated rows
AU - Colbourn, Charles J.
AU - Stinson, Douglas R.
AU - Veitch, Shannon
N1 - Publisher Copyright:
© 2019 Elsevier B.V.
Copyright:
Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/9
Y1 - 2019/9
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
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U2 - 10.1016/j.disc.2019.05.021
DO - 10.1016/j.disc.2019.05.021
M3 - Article
AN - SCOPUS:85066617377
VL - 342
SP - 2455
EP - 2466
JO - Discrete Mathematics
JF - Discrete Mathematics
SN - 0012-365X
IS - 9
ER -