Digital nets and sequences constructed over finite rings and their application to quasi-Monte Carlo integration |
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Authors: | Gerhard Larcher Harald Niederreiter Wolfgang Ch Schmid |
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Institution: | (1) Institut für Mathematik, Universität Salzburg, Hellbrunnerstrasse 34, A-5020 Salzburg, Austria;(2) Institut für Informationsverarbeitung, Österreichische Akademie der Wissenschaften, Sonnenfelsgasse 19, A-1010 Wien, Austria |
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Abstract: | A detailed study of digital (t, m, s)-nets and digital (T,s)-sequences constructed over finite rings is carried out. We present general existence theorems for digital nets and sequences and also explicit constructions. Special attention is devoted to the case where the finite ring is a residue class ring of the integers. This study is motivated by the problem of numerical integration of multivariate Walsh series by quasi-Monte Carlo methods, for which we also provide a general error bound.The third author was supported by the CEI Project PACT, WP5.1.2.1.3. |
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Keywords: | 11K38 11K45 42C10 65D30 |
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