Optimal Faure sequence via mix Faure with the best scrambling schemes

Behrouz Fathi-Vajargah, Elham Radmoghadam


The Faure sequence is one of the most well-known quasi-random sequences used in quasi-Monte Carlo applications. In its original and most basic form, the Faure sequence suffers from correlate different dimensions but when differences of sample size and dimension is high, the Faur sequence operates better than randomly scrambled version. In this paper we analyze various scrambling methods and propose a new method by mixing Faure sequence with the best available scrambled version. We demonstrate the usefulness of our method by integration problems.


Faure sequence; Low-discrepancy sequences; (quasi)-Monte Carlo; Linear scrambling; Nonlinear scrambling

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