Some new lower bounds to centered and wrap-round L2-discrepancies

We study the uniformity of two-level U-type designs based on the centered and wrap-around L2-discrepancies. Based on the known formulation of the measures of uniformity, we present some new lower bounds to centered and wrap-around L2-discrepancies, which can be used as benchmarks in searching uniform U-type designs or helping to proof that a good design is in fact uniform. Using the efficient algorithm proposed in Fang et al. (2003), some two-level uniform designs are obtained.