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)
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
On the L2-discrepancy for anchored boxes
Journal of Complexity
Complexity and information
The Mean Square Discrepancy of Scrambled (t,s)-Sequences
SIAM Journal on Numerical Analysis
The discrepancy and gain coefficients of scrambled digital nets
Journal of Complexity
Optimal quadrature for Haar wavelet spaces
Mathematics of Computation
Research Note: Generating parallel quasirandom sequences via randomization
Journal of Parallel and Distributed Computing
Efficient Generation of Parallel Quasirandom Faure Sequences Via Scrambling
ICCS '07 Proceedings of the 7th international conference on Computational Science, Part I: ICCS 2007
Computational investigations of scrambled Faure sequences
Mathematics and Computers in Simulation
Constructions of (t ,m,s)-nets and (t,s)-sequences
Finite Fields and Their Applications
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The computational complexity of the integration problem in terms of the expected error has recently been an important topic in Information-Based Complexity. In this setting, we assume some sample space of integration rules from which we randomly choose one. The most popular sample space is based on Owen's random scrambling scheme whose theoretical advantage is the fast convergence rate for certain smooth functions.This paper considers a reduction of randomness required for Owen's random scrambling by using the notion of i-binomial property. We first establish a set of necessary and sufficient conditions for digital (0,s)-sequences to have the i-binomial property. Then based on these conditions, the left and right i-binomial scramblings are defined. We show that Owen's key lemma (Lemma 4, SIAM J. Numer. Anal. 34 (1997) 1884) remains valid with the left i- binomial scrambling, and thereby conclude that all the results on the expected errors of the integration problem so far obtained with Owen's scrambling also hold with the left i-binomial scrambling.