Some Results on 2n - k Fractional Factorial Designs and Search for Minimum Aberration Designs

In this paper we find several interesting properties of 2ⁿ⁻ᵏ fractional factorial designs. An upper bound is given for the length of the longest word in the defining contrasts subgroup. We obtain minimum aberration 2ⁿ⁻ᵏ designs for $k = 5$ and any n. Furthermore, we give a method to test the equivalence of fractional factorial designs and prove that minimum aberration 2n - k designs for k ≤ 4 are unique.