In this paper, the problem of constructing optimal blocked regular
fractional factorial designs is considered. The concept of minimum aberration
due to Fries and Hunter is a wellaccepted criterion for selecting good
unblocked fractional factorial designs. Cheng, Steinberg and Sun showed that a
minimum aberration design of resolution three or higher maximizes the number of
twofactor interactions which are not aliases of main effects and also
tends to distribute these interactions over the alias sets very uniformly. We
extend this to construct block designs in which (i) no main effect is aliased
with any other main effect not confounded with blocks, (ii) the number of
twofactor interactions that are neither aliased with main effects nor
confounded with blocks is as large as possible and (iii) these interactions are
distributed over the alias sets as uniformly as possible. Such designs perform
well under the criterion of maximum estimation capacity, a criterion of model
robustness which has a direct statistical meaning. Some general results on the
construction of blocked regular fractional factorial designs with maximum
estimation capacity are obtained by using a finite projective geometric
approach.