Displaying similar documents to “Discrepancy and diaphony of digital (0,1)-sequences in prime base”

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...

Irreducible Sobol' sequences in prime power bases

Henri Faure, Christiane Lemieux (2016)

Acta Arithmetica

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Sobol' sequences are a popular family of low-discrepancy sequences, in spite of requiring primitive polynomials instead of irreducible ones in later constructions by Niederreiter and Tezuka. We introduce a generalization of Sobol' sequences that removes this shortcoming and that we believe has the potential of becoming useful for practical applications. Indeed, these sequences preserve two important properties of the original construction proposed by Sobol': their generating matrices...