Van der Corput sequences towards general (0,1)–sequences in base b
Journal de Théorie des Nombres de Bordeaux, Volume 19 (2007) no. 1, pp. 125-140.

As a result of recent studies on unidimensional low discrepancy sequences, we can assert that the original van der Corput sequences are the worst distributed with respect to various measures of irregularities of distribution among two large families of (0,1)–sequences, and even among all (0,1)–sequences for the star discrepancy D * . We show in the present paper that it is not the case for the extreme discrepancy D by producing two kinds of sequences which are the worst distributed among all (0,1)–sequences, with a discrepancy D essentially twice greater. In addition, we give an unified presentation for the two generalizations presently known of van der Corput sequences.

A la suite de travaux récents sur les suites à faible discrépance unidimensionnelles, on peut affirmer que les suites de van der Corput originales sont les plus mal distribuées pour diverses mesures d’irrégularités de distribution parmi deux grandes familles de (0,1)–suites, et même parmi toutes les (0,1)–suites pour la discrépance à l’origine D * . Nous montrons ici que ce n’est pas le cas pour la discrépance extrême D en produisant deux types de suites qui sont les plus mal distribuées parmi les (0,1)–suites, avec une discrépance D essentiellement deux fois plus grande. En outre, nous donnons une présentation unifiée pour les deux généralisations connues des suites de van der Corput.

Received:
Published online:
DOI: 10.5802/jtnb.577
Henri Faure 1

1 Institut de Mathématiques de Luminy, U.M.R. 6206 CNRS 163 avenue de Luminy, case 907 13288 Marseille Cedex 09, France
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Henri Faure. Van der Corput sequences towards general (0,1)–sequences in base b. Journal de Théorie des Nombres de Bordeaux, Volume 19 (2007) no. 1, pp. 125-140. doi : 10.5802/jtnb.577. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.577/

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