On scrambled Halton sequences Original Research Article

Haltonʹs 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∞L∞- and L2L2-discrepancies (D∗D∗ resp. T∗T∗), and by performing integration tests. Most investigated sequence types give practically equivalent results for D∗D∗, T∗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.