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Abstract
In this article we focus on two aspects of one-dimensional diaphony of generalised van der Corput sequences in arbitrary bases. First we give a permutation with the best distribution behaviour concerning the diaphony known so far. We improve a result of Chaix and Faure from 1993 from a value of 1.31574 . . . for a permutation in base 19 to 1.13794 . . . for our permutation in base 57. Moreover for an infinite sequence X and its symmetric version
, we analyse the connection between the diaphony F(X, N) and the L2-discrepancy
using another result of Chaix and Faure. Therefore we state an idea how to get a lower bound for the diaphony of generalised van der Corput sequences in arbitrary base b.
Keywords.: Diaphony; generalised van der Corput sequence
Received: 2009-12-01
Revised: 2010-09-22
Published Online: 2010-11-05
Published in Print: 2010-December
© de Gruyter 2010