Characterization of minimum aberration $2\sp {n-k}$ designs in terms of their complementary designs

Abstract

A general result is obtained that relates the word-length pattern of a $2^{n-k}$ design to that of its complementary design. By applying this result and using group isomorphism, we are able to characterize minimum aberration $2^{n-k}$ designs in terms of properties of their complementary designs. The approach is quite powerful for small values of $2^{n-k} - n - 1$. In particular, we obtain minimum aberration $2^{n-k}$ designs with $2^{n-k} - n - 1 = 1$ to 11 for any n and k.