Blocking in regular fractional factorials: a projective geometric approach

Abstract

A projective geometric characterization is given of the existence of any regular main effect $s^{n-k}$ design in $s^{\gamma}$ blocks. It leads to a constructive method for finding a maximal blocking scheme for any given fractional factorial design. A useful sufficient condition for admissible block designs is given in terms of the minimum aberration property of a certain unblocked design.