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 $(\gamma_j)_{j \ge 1}$ under the mildest condition on the weight sequence known so far for explicitly constructive sequences. The condition requires $\sup_{d \ge 1} \max_{\emptyset \not= \mathfrak{u} \subseteq [d]} \prod_{j \in \mathfrak{u}} (j \gamma_j) < \infty$. The same result holds for Niederreiter sequences and for other types of digital sequences. Our results are true also for the weighted unanchored discrepancy.