Tractability properties of the weighted star discrepancy of the Halton sequence.

Abstract We study the weighted star discrepancy of the Halton sequence. In particular, we show that the Halton sequence achieves strong polynomial tractability for the weighted star discrepancy for product weights (γ j) j ≥ 1 under the mildest condition on the weight sequence known so far for explicitly constructive sequences. The condition requires sup d ≥ 1 max 0̸ ≠ u ⊆ [ d ] ∏ j ∈ u (j γ j) < ∞. The same result holds for Niederreiter sequences and for other types of digital sequences. Our results are true also for the weighted unanchored discrepancy. [ABSTRACT FROM AUTHOR]