Low discrepancy polynomial lattice point sets

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.