There are various discrepancies that are measures of uniformity for a set of points on the unit hypercube. The discrepancies have played an important role in quasi-Monte Carlo methods. Each discrepancy has its own characteristic and some weakness. In this paper we point out some unreasonable phenomena associated with the commonly used discrepancies in the literature such as the L p-star discrepancy, the center L2-discrepancy (CD) and the wrap-around L2-discrepancy (WD). Then, a new discrepancy, called the mixture discrepancy (MD), is proposed. As shown in this paper, the mixture discrepancy is...
