A lower bound to the measure of optimality for main effect plans in the general asymmetric factorial experiments.

A design d is called D-optimal if it maximizes det(Md) and is called MS-optimal if it maximizes tr(Md) and minimizes tr[(Md)2] among those which maximize tr(Md), where Md stands for the information matrix produced from d under a given model. In this paper, we establish a lower bound for tr[(Md)2] with respect to a main effects model, where d is an s1×s2×···×sm levels asymmetric orthogonal array of strength at least 1. Nonisomorphic asymmetrical MS-optimal orthogonal arrays of strength 1 with N=6, 8 and 12 runs are also presented. [ABSTRACT FROM AUTHOR]