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Search: MSC category 05B15 ( Orthogonal arrays, Latin squares, Room squares )

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1. CMB 1999 (vol 42 pp. 359)

Martin, W. J.; Stinson, D. R.
A Generalized Rao Bound for Ordered Orthogonal Arrays and $(t,m,s)$-Nets
In this paper, we provide a generalization of the classical Rao bound for orthogonal arrays, which can be applied to ordered orthogonal arrays and $(t,m,s)$-nets. Application of our new bound leads to improvements in many parameter situations to the strongest bounds (\ie, necessary conditions) for existence of these objects.

Categories:05B15, 65C99

2. CMB 1998 (vol 41 pp. 33)

Gallant, Robert; Colbourn, Charles J.
Asymptotic existence of tight orthogonal main effect plans
Our main result is showing the asymptotic existence of tight $\OMEP$s. More precisely, for each fixed number $k$ of rows, and with the exception of $\OMEP$s of the form $2 \times 2 \times \cdots 2 \times 2s\specdiv 4s$ with $s$ odd and with more than three rows, there are only a finite number of tight $\OMEP$ parameters for which the tight $\OMEP$ does not exist.

Categories:62K99, 05B15

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