Sinescu, V. & Joe, S.(2008). Good lattice rules with a composite number of points based on the product weighted star discrepancy. In H. Niederreiter & D. Talay (Eds), Monte Carlo and Quasi-Monte Carlo Methods 2006(pp. 645-658). Berlin, Germany: Springer.
Permanent Research Commons link: https://hdl.handle.net/10289/2004
Rank-1 lattice rules based on a weighted star discrepancy with weights of a product form have been previously constructed under the assumption that the number of points is prime. Here, we extend these results to the non-prime case. We show that if the weights are summable, there exist lattice rules whose weighted star discrepancy is O(n−1+δ), for any δ > 0, with the implied constant independent of the dimension and the number of lattice points, but dependent on δ and the weights. Then we show that the generating vector of such a rule can be constructed using a component-by-component (CBC) technique. The cost of the CBC construction is analysed in the final part of the paper.
Springer Berlin Heidelberg
This is an author’s version of article published in the book: Monte Carlo and Quasi-Monte Carlo Methods 2006.