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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, 19 no. 1 (2007), p. 125-140, doi: 10.5802/jtnb.577
Article PDF | Reviews Zbl 1119.11044

Résumé - Abstract

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.

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