Some properties of blocked and unblocked foldovers of 2^k-p designs

In this article, we focus on the theoretical properties of the foldover design and the resulting combined design obtained by augmenting an initial design by its foldover. We prove that there are 2^p distinct ways to fold over a 2^k-p design. Optimal foldover plans are also discussed. We investigate the impact of the inclusion of a blocking variable to the design. We show that the minimum aberration foldover design with the presence of the blocking effect is the same as the one without blocking.