Some results on generalized minimum aberration for symmetrical fractional factorial designs

Generalized minimum aberration of fractional factorial designs has popularly been discussed. Recently, Lu et al. (Technical Report-324, 2002) proposed a so-called nearest balance criterion, which extends the V-criterion studied by Tang (Biometrika, 88 (2001) 401) for two-level designs to multi-level designs, to evaluate fractional factorials. In this paper, that generalized minimum aberration coincides with nearest balance for symmetrical factorials is reported, which is a generalization of the related results in Tang (2001). Our results not only further provide a projection interpretation of generalized minimum aberration in terms of level combinations but they also give a theoretical justification of the nearest balance criterion. A lower bound of generalized word length pattern for symmetrical factorials is also obtained. (C) 2003 Elsevier B.V. All rights reserved.