2 n-l designs with weak minimum aberration

Since not all 2ⁿ⁻¹ fractional factorial designs with maximum resolution are equally good, Fries and Hunter introduced the minimum aberration criterion for selecting good 2ⁿ⁻¹ fractional factorial designs with the same resolution. We modify the concept of minimum aberration and define weak minimum aberration and show the usefulness of this new design concept. Using some techniques from finite geometry, we construct 2ⁿ⁻¹ fractional factorial designs of resolution III with weak minimum aberration. Further, several families of 2ⁿ⁻¹ fractional factorial designs of resolution III and IV with minimum aberration are obtained.