The inverse of the star-discrepancy depends linearly on the dimension

156 citations recorded by the source corpus.

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Discrepancy Theory and Quasi-Monte Carlo Integration (2014, unknown): “It was shown in Sloan and Woźniakowski [107] and Woźniakowski [113] (in a much more general setting) that for ε ∈ (0, 1) we have N2(s, ε) ≥ (1− ε2) ( 9 8 )s .”
Hyperbolic Cross Approximation (2016, background): “Via probabilistic arguments based on deep results from the theory of empirical processes (Dudley 1984, Talagrand 1994) and combinatorics (Haussler 1995) the authors in [172] proved the existence of a universal (but unknown) constant c > 0 such that for arbitrary dimension d ∈ N”
Tractability of Multivariate Problems (2008, background): “Therefore it was quite a surprise when a positive result was proved in [116].”
Digital Nets and Sequences: Discrepancy Theory and Quasi-Monte Carlo Integration (2010, methodology): “This result, which was also shown first in [93], has the advantage that its proof is more or less elementary and that it contains no unknown constants.”
Greedy approximation (2008, background): “There are also some other estimates in Heinrich et al. (2001) with explicit constants.”