Optimal foldover plans of three-level designs with minimum wrap-around L 2-discrepancy

Abstract

The objective of this paper is to study the issue of employing the uniformity criterion measured by the wrap-around L 2-discrepancy to assess the optimal foldover plans for three-level designs. For three-level fractional factorials as the original designs, the general foldover plan and combined design under a foldover plan are defined, some theoretical properties of the defined foldover plans are obtained, a tight lower bound of the wrap-around L 2-discrepancy of combined designs under a general foldover plan is also obtained, which can be used as a benchmark for searching optimal foldover plans. For illustration of the usage of our theoretical results, a catalog of optimal foldover plans for uniform initial designs with s three-level factors is tabulated, where 2 ⩽ s ⩽ 11.