081  Berichtsreihe des Mathematischen Seminars der Universität Kiel  
Benjamin Doerr, Michael Gnewuch, Peter Kritzer, Friedrich Pillichshammer:Componentbycomponent construction of lowdiscrepancy point sets of small sizeWe investigate the problem of constructing small point sets with low star discrepancy in the $s$dimensional unit cube. The size of the point set shall always be polynomial in the dimension $s$. Our particular focus is on extending the dimension of a given lowdiscrepancy point set. This results in a deterministic algorithm that constructs $N$point sets with small discrepancy in a componentbycomponent fashion. The algorithm also provides the exact star discrepancy of the output set. Its runtime considerably improves on the runtimes of the currently known deterministic algorithms that generate lowdiscrepancy point sets of comparable quality. We also study infinite sequences of points with infinitely many components such that all initial subsegments projected down to all finite dimensions have low discrepancy. To this end, we introduce the inverse of the star discrepancy of such a sequence, and derive upper bounds for it as well as for the star discrepancy of the projections of finite subsequences with explicitly given constants. In particular, we establish the existence of sequences whose inverse of the star discrepancy depends linearly on the dimension. Mathematics Subject Classification (1991): 11K38 Bibliographical note: vom Journal Monte Carlo Methods and Applications angenommen Keywords: Star discrepancy, multivariate integration, derandomization

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