A note on optimal point distributions in [0,1)s

Authors:
Gerhard Larcher;Friedrich Pillichshammer
Affiliations:
Institut für Finanzmathematik, Universität Linz, Altenbergerstraíe 69, A-4040 Linz, Austria;Institut für Finanzmathematik, Universität Linz, Altenbergerstraíe 69, A-4040 Linz, Austria
Venue:
Journal of Computational and Applied Mathematics
Year:
2007

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Abstract

In this note we determine the infimum of the L"2-, the star- and the extreme discrepancy taken over all 2-element point sets in the s-dimensional unit cube. Moreover we give very good bounds on the infimum of the isotropic discrepancy taken over all (s+1)-element point sets in [0,1)^s.