Bounds for orthogonal arrays with repeated rows
Combinatorics
2018-12-14 v1
Abstract
In this expository paper, we mainly study orthogonal arrays (OAs) of strength two having a row that is repeated times. It turns out that the Plackett-Burman bound (\cite{PB}) can be strengthened by a factor of for orthogonal arrays of strength two that contain a row that is repeated times. This is a consequence of a more general result due to Mukerjee, Qian and Wu \cite{Muk} that applies to orthogonal arrays of arbitrary strength . We examine several proofs of the Plackett-Burman bound and discuss which of these proofs can be strengthened to yield the aforementioned bound for OAs of strength two with repeated rows. We also briefly discuss related bounds for -designs, and OAs of strength , when .
Cite
@article{arxiv.1812.05145,
title = {Bounds for orthogonal arrays with repeated rows},
author = {Douglas R. Stinson},
journal= {arXiv preprint arXiv:1812.05145},
year = {2018}
}