The foldover is a quick and useful technique in construction of fractional factorial designs, which typically releases aliased factors or interactions. The issue of employing the uniformity criterion measured by the centered L2-discrepancy to assess the optimal foldover plans was studied for four-level design. A new analytical expression and a new lower bound of the centered L2-discrepancy for fourlevel combined design under a general foldover plan are respectively obtained. A necessary condition
for the existence of an optimal foldover plan meeting this lower bound was described. An algorithm for
searching the optimal four-level foldover plans is also developed. Illustrative examples are provided,
where numerical studies lend further support to our theoretical results. These results may help to
provide some powerful and efficient algorithms for searching the optimal four-level foldover plans.