Algorithm 823

Algorithm 823: Implementing scrambled digital sequences. Random scrambling of deterministic (t, m, s)-nets and (t, s)-sequences eliminates their inherent bias while retaining their low-discrepancy properties. This article describes an implementation of two types of random scrambling, one proposed by Owen and another proposed by Faure and Tezuka. The four different constructions of digital sequences implemented are those proposed by Sobol’, Faure, Niederreiter, and Niederreiter and Xing. Because the random scrambling involves manipulating all digits of each point, the code must be written carefully to minimize the execution time. Computed root mean square discrepancies of the scrambled sequences are compared to known theoretical results. Furthermore, the performances of these sequences on various test problems are discussed. (Source:

This software is also peer reviewed by journal TOMS.

References in zbMATH (referenced in 35 articles , 1 standard article )

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  1. Todorov, Venelin; Dimov, Ivan: Efficient stochastic approaches for multidimensional integrals in Bayesian statistics (2020)
  2. Harase, Shin: Comparison of Sobol’ sequences in financial applications (2019)
  3. Jiménez Rugama, Lluís Antoni; Gilquin, Laurent: Reliable error estimation for Sobol’ indices (2018)
  4. Cambou, Mathieu; Hofert, Marius; Lemieux, Christiane: Quasi-random numbers for copula models (2017)
  5. Gerber, Mathieu; Bornn, Luke: Improving simulated annealing through derandomization (2017)
  6. Heitsch, H.; Leövey, H.; Römisch, W.: Are quasi-Monte Carlo algorithms efficient for two-stage stochastic programs? (2016)
  7. Löhndorf, Nils: An empirical analysis of scenario generation methods for stochastic optimization (2016)
  8. Dimov, Ivan; Georgieva, Rayna: Multidimensional sensitivity analysis of large-scale mathematical models (2013)
  9. Hickernell, Fred J.; Jiang, Lan; Liu, Yuewei; Owen, Art B.: Guaranteed conservative fixed width confidence intervals via Monte Carlo sampling (2013)
  10. Talke, Ismael S.; Borkowski, John J.: Generation of space-filling uniform designs in unit hypercubes (2012)
  11. Baldeaux, Jan; Dick, Josef: A construction of polynomial lattice rules with small gain coefficients (2011)
  12. Atanassov, Emanouil; Karaivanova, Aneta; Ivanovska, Sofiya: Tuning the generation of Sobol sequence with Owen scrambling (2010)
  13. Dick, Josef; Pillichshammer, Friedrich: Digital nets and sequences. Discrepancy theory and quasi-Monte Carlo integration. (2010)
  14. Chi, Hongmei: Parallel quasirandom number generations for heterogeneous computing environments (2009)
  15. Genz, Alan; Bretz, Frank: Computation of multivariate normal and (t) probabilities (2009)
  16. L’Ecuyer, Pierre: Quasi-Monte Carlo methods with applications in finance (2009)
  17. Singhee, Amith; Rutenbar, Rob A.: Novel algorithms for fast statistical analysis of scaled circuits (2009)
  18. Ferm, Lars; Lötstedt, Per; Hellander, Andreas: A hierarchy of approximations of the master equation scaled by a size parameter (2008)
  19. Hickernell, Fred J.; Dick, Josef: An algorithm-driven approach to error analysis for multidimensional integration (2008)
  20. Ökten, Giray; Salta, Emmanuel; Göncü, Ahmet: On pricing discrete barrier options using conditional expectation and importance sampling Monte Carlo (2008)

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