An algorithm for generating all possible 2(p-q) fractional factorial designs and its use in scientific experimentation

An algorithm and computer program are presented for generating all the distinct 2(p-q) fractional factorial designs. Some applications of this algorithm to the construction of tables of designs and of designs for nonstandard situations and its use in Bayesian design are discussed. An appendix includes a discussion of an actual experiment whose design was facilitated by the algorithm.