Very large fractional factorial and central composite designs

We present a concise representation of fractional factorials and an algorithm to quickly generate resolution V designs. The description is based on properties of a complete, orthogonal discrete-valued basis set called Walsh functions. We tabulate two-level resolution V fractional factorial designs, as well as central composite designs allowing estimation of full second-order models, for experiments involving up to 120 factors. The simple algorithm provided can be used to characterize even larger designs, and a fast Walsh transform method quickly generates design matrices from our representation.