Some Results on sⁿ⁻ᵏ Fractional Factorial Designs with Minimum Aberration or Optimal Moments

The minimum aberration criterion is commonly used for selecting good fractional factorial designs. In this paper we obtain minimum aberration 2n - k designs for $k = 3, 4$ and any n. For $k > 4$ analogous results are not available for general n since the resolution criterion is not periodic for general n and $k > 4$. However, it can be shown that for any fixed k, both the resolution criterion and the minimum aberration criterion have a periodicity property in n for sn - k designs with large n. Furthermore, the optimal-moments criterion is periodic for any n and k.