Optimal periodic \(L_2\)-discrepancy and diaphony bounds for higher order digital sequences
type: Item
instance of: scholarly article
title: Optimal periodic \(L_2\)-discrepancy and diaphony bounds for higher order digital sequences
author: Friedrich Pillichshammer
published in: Acta Mathematica Hungarica
publication date: 2023-04-04T00:00:00Z
full work available at URL: https://arxiv.org/abs/2212.05747
Mathematics Subject Classification ID: 11K38
Mathematics Subject Classification ID: 11K06
Mathematics Subject Classification ID: 11K45
zbMATH DE Number: 7672148
zbMATH Keywords: periodic \(L_2\)-discrepancy
zbMATH Keywords: diaphony
zbMATH Keywords: explicit construction
zbMATH Keywords: digital sequence
zbMATH Keywords: higher order sequence
MaRDI profile type: Publication
OpenAlex ID: W4323663088
cites work: Q4726347
cites work: Discrépance et diaphonie en dimension un
cites work: Explicit Constructions of Quasi-Monte Carlo Rules for the Numerical Integration of High-Dimensional Periodic Functions
cites work: Walsh Spaces Containing Smooth Functions and Quasi–Monte Carlo Rules of Arbitrary High Order
cites work: Optimal \(L_{p}\)-discrepancy bounds for second order digital sequences
cites work: A note on the periodic \(L_2\)-discrepancy of Korobov's \(p\)-sets
cites work: Q3160669
cites work: Optimal \(\mathcal {L}_{2}\) discrepancy bounds for higher order digital sequences over the finite field \(\mathbb {F}_{2}\)
cites work: Discrepancy and diaphony of digital (0,1)-sequences in prime base
cites work: From van der Corput to modern constructions of sequences for quasi-Monte Carlo rules
cites work: On the diaphony of one class of one-dimensional sequences
cites work: Q4488050
cites work: Extreme and periodic $L_2$ discrepancy of plane point sets
cites work: Optimal quasi-Monte Carlo rules on order 2 digital nets for the numerical integration of multivariate periodic functions
cites work: Optimal Point Sets for Quasi-Monte Carlo Integration of Bivariate Periodic Functions with Bounded Mixed Derivatives
cites work: Asymptotic behavior of average \(L_p\)-discrepancies
cites work: Diaphony, a measure of uniform distribution, and the Patterson function
cites work: On Proinov's lower bound for the diaphony
cites work: Exact order of extreme \(L_p\) discrepancy of infinite sequences in arbitrary dimension
cites work: Point sets with optimal order of extreme and periodic discrepancy
cites work: Q4767350
cites work: On two versions of \(L^ 2\)-discrepancy and geometrical interpretation of diaphony
cites work: Q4254718
cites work: Geometric discrepancy. An illustrated guide
cites work: Point sets and sequences with small discrepancy
cites work: Q4003879
cites work: Low-discrepancy sequences and global function fields with many rational places
cites work: Van der Corput sequences, Kakutani transforms and one-dimensional numerical integration
cites work: A good permutation for one-dimensional diaphony
cites work: Symmetrization of the van der Corput generalized sequences
cites work: On the diaphony of the van der Corput-Halton sequence
cites work: On irregularities of distribution
cites work: Q4127854
DOI: 10.1007/S10474-023-01307-9
description: scientific article; zbMATH DE number 7672148