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

• Autorzy: Henri Faure , Friedrich Pillichshammer
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 11K38: Irregularities of distribution, discrepancy
• 11K31: Special sequences

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 2013
• Tom: 158
• Numer: 4
• Strony: 321-340

Daty

wydano

2013

Twórcy

autor

Henri Faure

• Institut de Mathématiques de Luminy (CNRS), Université d'Aix-Marseille, 163 avenue de Luminy, case 907, 13288 Marseille Cedex 09, France

autor

Friedrich Pillichshammer

• Institut für Finanzmathematik, Universität Linz, Altenbergerstraße 69, A-4040 Linz, Austria

Identyfikatory

DOI

10.4064/aa158-4-2