1. CMB 1999 (vol 42 pp. 359)
|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.
2. CMB 1998 (vol 41 pp. 33)
|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.