Abstract
The foldover is a useful technique in construction of two-level factorial designs. A foldover design is the follow-up experiment generated by reversing the sign(s) of one or more factors in the initial design. The full design obtained by joining the runs in the foldover design to those of the initial design is called the combined design. In this paper, some lower bounds of various discrepancies of combined designs, such as centered L2-discrepancy, symmetric L2-discrepancy and wrap-around L2-discrepancy, under a general foldover plan are obtained, which can be used as a benchmark for searching optimal foldover plans. Our results provide a theoretical justification for optimal foldover plans in terms of uniformity criterion.
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