Optimal foldover plans of asymmetric factorials with minimum wrap-around \[L_2\] -discrepancy

Literatures reveal that foldover is a useful technique in construction of factorial designs. 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 asymmetric fractional factorials. A general foldover strategy and combined design under a foldover plan are developed for asymmetric fractional factorials, some theoretical properties on the equivalence between the defined foldover plan and its complementary foldover plan are discussed. A new lower bound for the wrap-around \[L_2\]-discrepancy of combined designs 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.