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Digital Sequences with Best Possible Order of L2-Discrepancy

Part of: Probabilistic theory: distribution modulo $1$; metric theory of algorithms

Published online by Cambridge University Press:  21 December 2009

Friedrich Pillichshammer
Friedrich Pillichshammer
Affiliation:
Institut für Finanzmathematik, Universität Linz, Altenbergstraße 69, A-4040 Linz, Austria. E-mail: friedrich.pillichshammer@jku.at
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Abstract

This paper treats the L2-discrepancy of digital (0, 1)-sequences over ℤ2, and gives conditions on the generator matrix of such a sequence which guarantee minimal possible order of L2-discrepancy of the generated sequence. The existence is proved for the first time of digital (0; 1)-sequences over ℤ2 with L2-discrepancy of order . This order is best possible by a result of K. Roth. The existence proof is constructive.

MSC classification

Secondary: 11K38: Irregularities of distribution, discrepancy 11K36: Well-distributed sequences and other variations
Type
Research Article
Information
Mathematika , Volume 53 , Issue 1 , June 2006 , pp. 149 - 160
Copyright
Copyright © University College London 2006

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