Discrepancy and diaphony of digital (0,1)-sequences in prime base
Henri Faure (2005)
Acta Arithmetica
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Henri Faure (2005)
Acta Arithmetica
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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...
Mauro Torelli (2006)
RAIRO - Theoretical Informatics and Applications
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Increasing integer sequences include many instances of interesting sequences and combinatorial structures, ranging from tournaments to addition chains, from permutations to sequences having the that any integer greater than 1 can be obtained as the sum of two elements in the sequence. The paper introduces and compares several of these classes of sequences, discussing recurrence relations, enumerative problems and questions concerning shortest sequences.
Mercer, A.McD. (1978)
International Journal of Mathematics and Mathematical Sciences
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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...
Henri Faure, Christiane Lemieux (2012)
Acta Arithmetica
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Harald Niederreiter (2009)
Acta Arithmetica
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Hans Carstens (1975)
Fundamenta Mathematicae
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Roswitha Hofer, Gerhard Larcher (2010)
Acta Arithmetica
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Benito, Manuel, Creyaufmüller, Wolfgang, Varona, Juan L., Zimmermann, Paul (2002)
Experimental Mathematics
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C. Zaremba (1963)
Applicationes Mathematicae
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(2012)
Acta Arithmetica
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Jovan D. Kečkić (1973)
Publications de l'Institut Mathématique
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