Abstract
In this paper, we study a countable family of uniformly distributed sequences of partitions, called LS-sequences of partitions, and we give a precise estimate of their discrepancy. Among these sequences, we identify a countable class having low discrepancy (which means of order \({{\frac{1}{N}}}\)). We describe an explicit algorithm that associates to each of these sequences a uniformly distributed sequence of points (we call LS-sequences of points). The main result of this paper says that the discrepancy of the sequences of points associated by our algorithm to the LS-sequences of partitions is of order α N log N, if α N is the discrepancy of the corresponding sequence of partitions. We obtain therefore, in particular, a countable family of low-discrepancy sequences of points.
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Carbone, I. Discrepancy of LS-sequences of partitions and points. Annali di Matematica 191, 819–844 (2012). https://doi.org/10.1007/s10231-011-0208-z
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DOI: https://doi.org/10.1007/s10231-011-0208-z