Characterization of minimum aberration 2 n-k designs in terms of their complementary designs

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