Minimum aberration majorization in non-isomorphic saturated designs

In this paper we propose a new criterion, minimum aberration majorization, for comparing non-isomorphic saturated designs. This criterion is based on the generalized word-length pattern proposed by Ma and Fang (Metrika 53 (2001) 85) and Xu and Wu (Ann. Statist. 29 (2001) 1066) and majorization theory. The criterion has been successfully applied to check non-isomorphism and rank order saturated designs. Examples are given through five non-isomorphic L₁₆(2¹⁵) designs and two L₂₇(3¹³) designs.