Optimal foldover plans for regular s-level fractional factorial designs

This article introduces a general decomposition structure of the foldover plan. While all the previous work is limited to two-level designs, our results here are good for general regular s-level fractional factorial designs, where s is any prime or prime power. The relationships between an initial design and its combined designs are studied. This is done for both with and without consideration of the blocking factor. For illustration of the usage of our theorems, a complete collection of foldover plans for regular three-level designs with 27 runs is given that is optimal for aberration and clear effect numbers.