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Regular factorial designs with randomization restrictions are widely used inpractice. This paper provides a unified approach to the construction of suchdesigns using randomization defining contrast subspaces for the representationof randomization restrictions. We use finite projective geometry to determinethe existence of designs with the required structure and develop a systematicapproach for their construction. An attractive feature is that commonly usedfactorial designs with randomization restrictions are special cases of thisgeneral representation. Issues related to the use of these designs forparticular factorial experiments are also addressed.

Existence and construction of randomization defining contrast subspaces for regular factorial designs