TY - JOUR
T1 - Constructions of optimal orthogonal arrays with repeated rows
AU - Colbourn, Charles J.
AU - Stinson, Douglas R.
AU - Veitch, Shannon
N1 - Funding Information:
C.J. Colbourn's research is supported by the U.S. National Science Foundation grant #1813729.D.R. Stinson's research is supported by NSERC discovery grant RGPIN-03882. This work benefitted from the use of the CrySP RIPPLE Facility at the University of Waterloo. Also, we would like to thank Sophie Toulouse for bringing this problem to our attention. The authors declare that they have no conflict of interest.
Publisher Copyright:
© 2019 Elsevier B.V.
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 -