Abstract
The star discrepancy is a quantity for measuring the uniformity of a set of quadrature points and appears in the Koksma-Hlawka inequality. For integrals over [0, 1]d it is known that there exist d-dimensional rank-1 lattice rules having 0(n -1(ln(n))d) star discrepancy, where n is the number of points. Here we show that for n prime such rules may be obtained by constructing their generating vectors component by component. The rules are constructed to satisfy certain bounds on a quantity known as R. Bounds on the star discrepancy in terms of R then yield the desired O(n -1(In(n))d) star discrepancy.
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