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Average distance between consecutive points of uniformly distributed sequences

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Author(s): Friedrich Pillichshammer | Stefan Steinerberger

Journal: Uniform Distribution Theory
ISSN 1336-913X

Volume: 4;
Issue: 1;
Start page: 51;
Date: 2009;
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Keywords: Uniform distribution | van der Corput sequence | (n alpha)-sequence.

ABSTRACT
In this paper we give best possible lower and upper bounds on the average distance between consecutive points of uniformly distributed sequences. The upper bound is attained with the dyadic van der Corput sequence. Furthermore we give a constructive proof that any element from the interval $[0,1/2]$ can be obtained as the average distance between consecutive points of some uniformly distributed sequence.
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