Theory of optimal blocking of 2(n-m) designs

In this paper, we define the blocking wordlength pattern of a blocked fract ional factorial design by combining the wordlength patterns of treatment-de fining words and block-defining words. The concept of minimum aberration ca n be defined in terms of the blocking wordlength pattern and provides a goo d measure of the estimation capacity of a blocked fractional factorial desi gn. By blending techniques of coding theory and finite projective geometry, we obtain combinatorial identities that govern the relationship between th e blocking wordlength pattern of a blocked 2(n-m) design and the split word length pattern of its blocked residual design. Based on these identities, w e establish general rules for identifying minimum aberration blocked 2(n-m) designs in terms of their blocked residual designs. Using these rules, we study the structures of some blocked 2(n-m) designs with minimum aberration .