A Lower Bound for the Wrap-around L2-discrepancy on Combined Designs of Mixed Two- and Three-level Factorials

Abstract

The objective of this article is to study the issue of employing the uniformity criterion measured by wrap-around L2-discrepancy to assess the optimal foldover plans. For mixed two- and three-level fractional factorials as the original designs, general foldover plan and combined design under a foldover plan are defined, and the equivalence between any foldover plan and its complementary foldover plan is investigated. A lower bound of wrap-around L2-discrepancy of combined designs under a general foldover plan is obtained, which can be used as a benchmark for searching optimal foldover plans. Moreover, it also provides a theoretical justification for optimal foldover plans in terms of uniformity criterion.