Construction results on minimum aberration blocking schemes for 2m designs

This paper considers constructing minimum aberration blocking schemes for 2m designs. A blocking scheme is said to have estimability of order e if e is the greatest integer such that no effect involving e or less factors is aliased with a block effect. We observe that a minimum aberration blocking scheme with estimability of order e uniquely corresponds to a minimum aberration design of resolution R=e+1 and vice versa. Two implications follow immediately from this result. First, all existing minimum aberration designs of resolution III or higher can be used to obtain minimum aberration blocking schemes with estimability of order 2 or higher. Second, resolution II designs of minimum aberration are now of both theoretical and practical importance as they provide solutions to minimum aberration blocking schemes with estimability of order 1. We study the construction of minimum aberration designs of resolution II, and obtain a complete solution to the problem.