Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
The mean square discrepancy of randomized nets
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Quadrature Error Bounds with Applications to Lattice Rules
SIAM Journal on Numerical Analysis
Monte Carlo Variance of Scrambled Net Quadrature
SIAM Journal on Numerical Analysis
When are quasi-Monte Carlo algorithms efficient for high dimensional integrals?
Journal of Complexity
Scrambling sobol' and niederreiter-xing points
Journal of Complexity
Bounds for the weighted Lp discrepancy and tractability of integration
Journal of Complexity
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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 L2 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.