Improved discrepancy bounds for hybrid sequences involving Halton sequences
(2012)
Acta Arithmetica
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Displaying similar documents to “Substitutions and 1/2-discrepancy of nθ + x”
Improved discrepancy bounds for hybrid sequences involving Halton sequences
On existence and discrepancy of certain digital Niederreiter-Halton sequences
Roswitha Hofer, Gerhard Larcher (2010)
Acta Arithmetica
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A generalization of NUT digital (0,1)-sequences and best possible lower bounds for star discrepancy
Henri Faure, Friedrich Pillichshammer (2013)
Acta Arithmetica
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In uniform distribution theory, discrepancy is a quantitative measure for the irregularity of distribution of a sequence modulo one. At the moment the concept of digital (t,s)-sequences as introduced by Niederreiter provides the most powerful constructions of s-dimensional sequences with low discrepancy. In one dimension, recently Faure proved exact formulas for different notions of discrepancy for the subclass of NUT digital (0,1)-sequences. It is the aim of this paper to generalize...
L₂ discrepancy of generalized two-dimensional Hammersley point sets scrambled with arbitrary permutations
Henri Faure, Friedrich Pillichshammer, Gottlieb Pirsic, Wolfgang Ch. Schmid (2010)
Acta Arithmetica
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Improvements on the star discrepancy of (t,s)-sequences
Henri Faure, Christiane Lemieux (2012)
Acta Arithmetica
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The inverse of the star-discrepancy depends linearly on the dimension
Stefan Heinrich, Henryk Woźniakowski, Grzegorz W. Wasilkowski, Erich Novak (2001)
Acta Arithmetica
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An L¹ estimate for half-space discrepancy
William W. L. Chen, Giancarlo Travaglini (2011)
Acta Arithmetica
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Edmund Hlawka (1916-2009)
Wolfgang M. Schmidt (2009)
Acta Arithmetica
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Corrigendum to: "Improvements on the star discrepancy of (t,s)-sequences" (Acta Arith. 154 (2012), 61-78)
Henri Faure, Christiane Lemieux (2013)
Acta Arithmetica
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This short note is intended to correct an inaccuracy in the proof of Theorem 3 in the paper mentioned in the title. The result of Theorem 3 remains true without any other change in the proof. Furthermore, a misprint is pointed out.
A new construction of (t,s)-sequences and some improved bounds on their quality parameter
David J. S. Mayor, Harald Niederreiter (2007)
Acta Arithmetica
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General Discrepancy Estimates III: The Erdös-Turán-Koksma Inequality for the Haar Function System.
Peter Hellekalek (1995)
Monatshefte für Mathematik
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On the discrepancy of some hybrid sequences
Harald Niederreiter (2009)
Acta Arithmetica
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Discrepancy and diaphony of digital (0,1)-sequences in prime base
Henri Faure (2005)
Acta Arithmetica
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-discrepancy and statistical independence of sequences
Peter J. Grabner, Oto Strauch, Robert Franz Tichy (1999)
Czechoslovak Mathematical Journal
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We characterize statistical independence of sequences by the -discrepancy and the Wiener -discrepancy. Furthermore, we find asymptotic information on the distribution of the -discrepancy of sequences.
On the Star-Discrepancy of Generalized Hammersley Sequences in Two Dimensions.
H. Faure (1986)
Monatshefte für Mathematik
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An improved result on irregularities in distribution of sequences of integers
John H. Hodges (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti
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In 1972 the author used a result of K.F. Roth on irregularities in distribution of sequences of real numbers to prove an analogous result related to the distribution of sequences of integers in prescribed residue classes. Here, a 1972 result of W.M. Schmidt, which is an improvement of Roth's result, is used to obtain an improved result for sequences of integers.
An improved result on irregularities in distribution of sequences of integers
John H. Hodges (1988)
Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni
Similarity:
In 1972 the author used a result of K.F. Roth on irregularities in distribution of sequences of real numbers to prove an analogous result related to the distribution of sequences of integers in prescribed residue classes. Here, a 1972 result of W.M. Schmidt, which is an improvement of Roth's result, is used to obtain an improved result for sequences of integers.
On the correlation of families of pseudorandom sequences of k symbols
Kit-Ho Mak, Alexandru Zaharescu (2016)
Acta Arithmetica
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In an earlier paper Gyarmati introduced the notion of f-correlation for families of binary pseudorandom sequences as a measure of randomness in the family. In this paper we generalize the f-correlation to families of pseudorandom sequences of k symbols and study its properties.