Two- and three-level lower bounds for mixture L2-discrepancy and construction of uniform designs by threshold accepting

The uniform experimental design (UD), a major kind of space-filling design, is widely used in applications. The majority of UD tables (UDs) with good uniformity are generated under the centralized L2-discrepancy (CD) and the wrap-around L2-discrepancy (WD). Recently, the mixture L2-discrepancy (MD) is proposed and shown to be more reasonable than CD and WD in terms of uniformity. In this paper we review lower bounds for MD of two-level designs from a different point of view and provide a new lower bound. Following the same idea we obtain a lower bound for MD of three-level designs. Moreover, we construct UDs under the measurement of MD by the threshold accepting (TA) algorithm, and finally we attach two new UD tables with good properties derived from TA under the measurement of MD.