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# Association Schemes for Ordered Orthogonal Arrays and $(T,M,S)$-Nets

Published:1999-04-01
Printed: Apr 1999
• W. J. Martin
• D. R. Stinson
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## Abstract

In an earlier paper~\cite{stinmar}, we studied a generalized Rao bound for ordered orthogonal arrays and $(T,M,S)$-nets. In this paper, we extend this to a coding-theoretic approach to ordered orthogonal arrays. Using a certain association scheme, we prove a MacWilliams-type theorem for linear ordered orthogonal arrays and linear ordered codes as well as a linear programming bound for the general case. We include some tables which compare this bound against two previously known bounds for ordered orthogonal arrays. Finally we show that, for even strength, the LP bound is always at least as strong as the generalized Rao bound.
 MSC Classifications: 05B15 - Orthogonal arrays, Latin squares, Room squares 05E30 - Association schemes, strongly regular graphs 65C99 - None of the above, but in this section