Discrepancy bounds for infinite-dimensional order two digital sequences over \(\mathbb F_2\)

DOI10.1016/j.jnt.2013.09.012zbMath1286.11120arXiv1208.1308OpenAlexW2011523133MaRDI QIDQ2637186

Josef Dick

Publication date: 7 February 2014

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1208.1308

zbMATH Keywords

optimal convergence\(L_q\) discrepancyhigher order digital sequence

Mathematics Subject Classification ID

Irregularities of distribution, discrepancy (11K38) General theory of distribution modulo (1) (11K06) Pseudo-random numbers; Monte Carlo methods (11K45)

Related Items

Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions ⋮ On the upper bound of the $L_2$-discrepancy of Halton’s sequence ⋮ BMO and exponential Orlicz space estimates of the discrepancy function in arbitrary dimension ⋮ Optimal \(L_{p}\)-discrepancy bounds for second order digital sequences ⋮ The curse of dimensionality for the \(L_p\)-discrepancy with finite \(p\) ⋮ Central limit theorem for \((t,s)\)-sequences in base 2 ⋮ DISCREPANCY OF SECOND ORDER DIGITAL SEQUENCES IN FUNCTION SPACES WITH DOMINATING MIXED SMOOTHNESS ⋮ Discrepancy of Digital Sequences: New Results on a Classical QMC Topic ⋮ On the \(L_p\) discrepancy of two-dimensional folded Hammersley point sets ⋮ L_p- and S_p,q^rB-discrepancy of (order 2) digital nets ⋮ Exact order of extreme \(L_p\) discrepancy of infinite sequences in arbitrary dimension ⋮ Formulas for the Walsh coefficients of smooth functions and their application to bounds on the Walsh coefficients

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Point sets and sequences with small discrepancy
• Sequences, discrepancies and applications
• \(L_p\) discrepancy of generalized two-dimensional Hammersley point sets
• On the small ball inequality in all dimensions
• On the small ball inequality in three dimensions
• Low-discrepancy point sets
• Low-discrepancy and low-dispersion sequences
• Symmetrization of the van der Corput generalized sequences
• On the diaphony of the van der Corput-Halton sequence
• Low-discrepancy sequences and global function fields with many rational places
• Codes for the \(m\)-metric
• On the diaphony of one class of one-dimensional sequences
• A class of generalized Walsh functions
• Duality for digital nets and its applications
• Explicit constructions in the classical mean squares problem in irregularities of point distribution
• Optimal L₂discrepancy bounds for higher order digital sequences over the finite field F₂
• An effective proof of Roth's theorem on quadratic dispersion
• ON IRREGULARITIES OF DISTRIBUTION II
• On Quasi-Monte Carlo Rules Achieving Higher Order Convergence
• L 2 Discrepancy of Two-Dimensional Digitally Shifted Hammersley Point Sets in Base b
• Harmonic analysis on totally disconnected groups and irregularities of point distributions
• Orthogonality and Digit Shifts in the Classical Mean Squares Problem in Irregularities of Point Distribution
• Explicit Constructions of Quasi-Monte Carlo Rules for the Numerical Integration of High-Dimensional Periodic Functions
• Walsh Spaces Containing Smooth Functions and Quasi–Monte Carlo Rules of Arbitrary High Order
• Walsh-spectral test for GFSR pseudorandom numbers
• On irregularities of distribution, III
• On irregularities of distribution, IV
• On irregularities of distribution
• On the Numerical Integration of Walsh Series by Number-Theoretic Methods
• The Mean Square Discrepancy of Scrambled (t,s)-Sequences
• Discrépance et diaphonie en dimension un
• Polynomial arithmetic analogue of Halton sequences
• L₂discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations
• On the mean square weighted L₂discrepancy of randomized digital (t,m,s)-nets over Z₂
• On the Walsh Functions
• On irregularities of distribution
• Note on irregularities of distribution
• Geometric discrepancy. An illustrated guide
• Walsh series analysis of the \(L_2\)-discrepancy of symmetrized point sets

This page was built for publication: Discrepancy bounds for infinite-dimensional order two digital sequences over \(\mathbb F_2\)