Summary
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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© 2004 Springer-Verlag Berlin Heidelberg
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Joe, S. (2004). Component by Component Construction of Rank-1 Lattice Rules HavingO(n -1(In(n))d) Star Discrepancy. In: Niederreiter, H. (eds) Monte Carlo and Quasi-Monte Carlo Methods 2002. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-18743-8_17
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DOI: https://doi.org/10.1007/978-3-642-18743-8_17
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