On the root mean square weighted L2 discrepancy of scrambled nets

Until now (t,m,s)-nets in base b are the most important representatives in the family of low-discrepancy point sets. Such nets are often used for quasi-Monte Carlo approximation of high-dimensional integrals. Owen introduced a randomization of such point sets such that the net property is preserved. In this paper we consider the root mean square weighted L 2 discrepancy of (0,m,s)-nets in base b. The concept of weighted discrepancy was introduced by Sloan and Woźniakowski to give a general form of a Koksma-Hlawka inequality that takes into account imbalances in the "importance" of the projections of the integrand.

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