computational investigations of scrambled faure sequences

the faure sequence is one of the well-known quasi-random sequences used in quasi-monte carlo applications. in its original and most basic form, the faure sequence suffers from correlations between different dimensions. these correlations result in poorly distributed two-dimensional projections. a standard solution to this problem is to use a randomly scrambled version of the faure sequence. we analyze various scrambling methods and propose a new nonlinear scrambling method, which has similarities with inversive congruential methods for pseudo-random number generation. we demonstrate the usefulness of our scrambling by means of two-dimensional projections and integration problems.