A variant of Atanassov's method for \((t, s)\)-sequences and \((t, \mathbf{e}, s)\)-sequences

DOI10.1016/j.jco.2014.02.006zbMath1298.11075OpenAlexW2038559025MaRDI QIDQ2509950

Henri Faure, Christiane Lemieux

Publication date: 31 July 2014

Published in: Journal of Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jco.2014.02.006

zbMATH Keywords

star discrepancydiscrepancy boundsAtanassov's method\((t, \mathbf{e}, s)\)-sequences\((t, s)\)-sequences

Mathematics Subject Classification ID

Irregularities of distribution, discrepancy (11K38) General theory of distribution modulo (1) (11K06)

Related Items

From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules, Discrepancy of Digital Sequences: New Results on a Classical QMC Topic, Low-discrepancy sequences: Atanassov's methods revisited, Recent constructions of low-discrepancy sequences, A review of discrepancy bounds for \((t, s)\) and \((t, \mathbf{e}, s)\)-sequences with numerical comparisons, Halton-type sequences in rational bases in the ring of rational integers and in the ring of polynomials over a finite field, Generalized Hofer-Niederreiter sequences and their discrepancy from an \((\boldsymbol{U}, \boldsymbol{e}, s)\)-point of view, Irreducible Sobol’ sequences in prime power bases, Propagation rules for \((u, m, \mathbf{e}, s)\)-nets and \((u, \mathbf{e}, s)\)-sequences, Analysis of discrete least squares on multivariate polynomial spaces with evaluations at low-discrepancy point sets

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• New star discrepancy bounds for \((t,m,s)\)-nets and \((t,s)\)-sequences
• Point sets and sequences with small discrepancy
• On the efficiency of certain quasi-random sequences of points in evaluating multi-dimensional integrals
• Low-discrepancy sequences and global function fields with many rational places
• A construction of \((t,s)\)-sequences with finite-row generating matrices using global function fields
• On the discrepancy of generalized Niederreiter sequences
• Halton-type sequences from global function fields
• Improved upper bounds on the star discrepancy of \((t,m,s)\)-nets and \((t,s)\)-sequences
• Improvements on the star discrepancy of (t,s)-sequences
• Discrépance de suites associées à un système de numération (en dimension s)
• Polynomial arithmetic analogue of Halton sequences
• On the distribution of points in a cube and the approximate evaluation of integrals