Abstract
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 D N ⁎ satisfies a discrepancy bound of the type N D N ⁎ ⩽ c ( log N ) s − 1 log log N ( c a constant). This result is a substantial extension of an earlier result by Larcher.
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