Choice of optimal blocking schemes in two-level and three-level designs

Blocking is commonly used in design of experiments to reduce systematic variation and increase precision of effect estimation. For 2(n-k) designs in 2(p) blocks, others have studied the confounding pattern between blocking effects and treatment effects and proposed some criteria to choose optimal blocking schemes. We propose alternative criteria that allow estimation of more lower-order effects. Extensions to three-level fractional factorial design are considered, and tables of useful designs are given.