Low discrepancy polynomial lattice point sets

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• 作者：Peter Kritzer ; Friedrich Pillichshammer
• 关键词：11K38 ; 11K06 ; 15A99
• 刊名：Journal of Number Theory
• 出版年：2012
• 出版时间：November, 2012
• 年：2012
• 卷：132
• 期：11
• 页码：2510-2534
• 全文大小：317 K

文摘

Polynomial lattice point sets are polynomial versions of classical lattice point sets and among the most widely used classes of node sets in quasi-Monte Carlo integration algorithms. In this paper, we show the existence of s-dimensional polynomial lattice point sets with N points whose star discrepancy satisfies a discrepancy bound of the type (c a constant). This result is a substantial extension of an earlier result by Larcher.