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.