A generalization of NUT digital $(0,1)$-sequences
 and best possible lower bounds for star discrepancy

Henri Faure; Friedrich Pillichshammer

doi:10.4064/aa158-4-2

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A generalization of NUT digital $(0,1)$-sequences and best possible lower bounds for star discrepancy

Henri Faure ¹ ; Friedrich Pillichshammer ²

¹ Institut de Mathématiques de Luminy (CNRS) Université d'Aix-Marseille 163 avenue de Luminy, case 907 13288 Marseille Cedex 09, France
² Institut für Finanzmathematik Universität Linz Altenbergerstra{\OT 1ß}e 69 A-4040 Linz, Austria

Acta Arithmetica, Tome 158 (2013) no. 4, pp. 321-340.

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

Résumé

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 the concept of NUT digital $(0,1)$-sequences and to show in which sense Faure's formulas remain valid for this generalization. As an application we obtain best possible lower bounds for the star discrepancy of several subclasses of $(0,1)$-sequences.

DOI : 10.4064/aa158-4-2

Keywords: uniform distribution theory discrepancy quantitative measure irregularity distribution sequence modulo moment concept digital sequences introduced niederreiter provides powerful constructions s dimensional sequences low discrepancy dimension recently faure proved exact formulas different notions discrepancy subclass nut digital sequences paper generalize concept nut digital sequences which sense faures formulas remain valid generalization application obtain best possible lower bounds star discrepancy several subclasses sequences

Affiliations des auteurs :

Henri Faure ¹ ; Friedrich Pillichshammer ²

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 and best possible lower bounds for star discrepancy
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Henri Faure; Friedrich Pillichshammer. A generalization of NUT digital $(0,1)$-sequences
 and best possible lower bounds for star discrepancy. Acta Arithmetica, Tome 158 (2013) no. 4, pp. 321-340. doi : 10.4064/aa158-4-2. http://geodesic.mathdoc.fr/articles/10.4064/aa158-4-2/

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