Algebraic Approach for Enumerating Fractional Factorial Designs

Abstract

Constructing fractional factorial designs with given properties is one of important topics in design of experiments. In this paper, we give some results based on the technique of computational algebraic methods. For each fractional factorial design with given property, we characterize its polynomial indicator function and enumerate solutions of the algebraic equation for the coefficients of the corresponding indicator functions. By this approach, we can enumerate all the fractional factorial designs with given orthogonality for any size in theory. However, problems of computational feasibility arise in actual computations.