Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Quasi-random sequences and their discrepancies
SIAM Journal on Scientific Computing
Quadrature Error Bounds with Applications to Lattice Rules
SIAM Journal on Numerical Analysis
Efficient algorithms for computing the L2-discrepancy
Mathematics of Computation
Monte Carlo Variance of Scrambled Net Quadrature
SIAM Journal on Numerical Analysis
A generalized discrepancy and quadrature error bound
Mathematics of Computation
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Latin supercube sampling for very high-dimensional simulations
ACM Transactions on Modeling and Computer Simulation (TOMACS) - Special issue on uniform random number generation
Monto Carlo extension of quasi-Monte Carlo
Proceedings of the 30th conference on Winter simulation
Quasi-Monte Carlo methods in cash flow testing simulations
Proceedings of the 32nd conference on Winter simulation
Algorithm 823: Implementing scrambled digital sequences
ACM Transactions on Mathematical Software (TOMS)
Journal of Complexity
Variance with alternative scramblings of digital nets
ACM Transactions on Modeling and Computer Simulation (TOMACS)
I-binomial scrambling of digital nets and sequences
Journal of Complexity
Optimal quadrature for Haar wavelet spaces
Mathematics of Computation
On the root mean square weighted L2 discrepancy of scrambled nets
Journal of Complexity
Parameterization based on randomized quasi-Monte Carlo methods
Parallel Computing
Computational investigations of scrambled Faure sequences
Mathematics and Computers in Simulation
Mathematical and Computer Modelling: An International Journal
Constructions of (t ,m,s)-nets and (t,s)-sequences
Finite Fields and Their Applications
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One popular family of low dicrepancy sets is the (t, m, s)-nets. Recently a randomization of these nets that preserves their net property has been introduced. In this article a formula for the mean square L2-discrepancy of (0, m, s)-nets in base b is derived. This formula has a computational complexity of only O(s log(N) + s2) for large N or s, where N = bm is the number of points. Moreover, the root mean square L2-discrepancy of (0, m, s)-nets is show to be O(N-1[log(N)](s-1)/2) as N tends to infinity, the same asymptotic order as the known lower bound for the L2-discrepancy of an arbitrary set.