  Regular factorial designs with randomization restrictions are widely used in
practice. This paper provides a unified approach to the construction of such
designs using randomization defining contrast subspaces for the representation
of randomization restrictions. We use finite projective geometry to determine
the existence of designs with the required structure and develop a systematic
approach for their construction. An attractive feature is that commonly used
factorial designs with randomization restrictions are special cases of this
general representation. Issues related to the use of these designs for
particular factorial experiments are also addressed.
