Factorial designs are commonly used to assess the impact of factors and factor combinations in industrial and agricultural experiments. Though preferred, complete randomization of trials is often infeasible, and randomization restrictions are imposed. In this paper, we discuss a finite projective geometric (PG) approach to unify the existence, construction and analysis of multistage factorial designs with randomization restrictions using randomization defining contrast subspaces (or flats of a PG). Our main focus will be on the construction of such designs, and developing a word length pattern scheme that can be used for generalizing the traditional design rank- ing criteria for factorial designs. We also present a novel isomorphism check algorithm for these designs.