Journal Title
Title of Journal: Annali di Matematica
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Abbravation: Annali di Matematica Pura ed Applicata (1923 -)
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Publisher
Springer Berlin Heidelberg
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Authors: Christoph Aistleitner Markus Hofer Volker Ziegler
Publish Date: 2013/02/28
Volume: 193, Issue: 5, Pages: 1329-1344
Abstract
Ingrid Carbone introduced the notion of socalled LSsequences of points which are obtained by a generalization of Kakutani’s interval splitting procedure Under an appropriate choice of the parameters L and S such sequences have low discrepancy which means that they are natural candidates for QuasiMonte Carlo integration It is tempting to assume that LSsequences can be combined coordinatewise to obtain a multidimensional lowdiscrepancy sequence However in the present paper we prove that this is not always the case if the parameters L 1S 1 and L 2S 2 of two onedimensional lowdiscrepancy LSsequences satisfy certain numbertheoretic conditions then their twodimensional combination is not even dense in 012
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