Random number generation and quasi-Monte Carlo methods
Random number generation and quasi-Monte Carlo methods
Implementation and tests of low-discrepancy sequences
ACM Transactions on Modeling and Computer Simulation (TOMACS)
Quasi-random sequences and their discrepancies
SIAM Journal on Scientific Computing
Journal of Computational Physics
Monte Carlo Variance of Scrambled Net Quadrature
SIAM Journal on Numerical Analysis
Scrambling sobol' and niederreiter-xing points
Journal of Complexity
Algorithm 247: Radical-inverse quasi-random point sequence
Communications of the ACM
Algorithm 823: Implementing scrambled digital sequences
ACM Transactions on Mathematical Software (TOMS)
Discrepancy behaviour in the non-asymptotic regime
Applied Numerical Mathematics
Good permutations for deterministic scrambled Halton sequences in terms of L2-discrepancy
Journal of Computational and Applied Mathematics
Mathematical and Computer Modelling: An International Journal
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Halton's low discrepancy sequence is still very popular in spite of its shortcomings with respect to the correlation between points of two-dimensional projections for large dimensions. As a remedy, several types of scrambling and/or randomization for this sequence have been proposed. We examine empirically some of these by calculating their L"~- and L"2-discrepancies (D^* resp. T^*), and by performing integration tests. Most investigated sequence types give practically equivalent results for D^*, T^*, and the integration error, with two exceptions: random shift sequences are in some cases less efficient, and the shuffled Halton sequence is no more efficient than a pseudo-random one. However, the correlation mentioned above can only be broken with digit-scrambling methods, even though the average correlation of many randomized sequences tends to zero.