The Number of Lattice Rules of Specified Upper Class and Rank
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This is an author’s version of an article published in the journal: BIT Numerical Mathematics. © Springer Netherlands. The original publication is available at www.springerlink.com.
Abstract
The upper class of a lattice rule is a convenient entity for classification and other purposes. The rank of a lattice rule is a basic characteristic, also used for classification. By introducing a rank proportionality factor and obtaining certain recurrence relations, we show how many lattice rules of each rank exist in any prime upper class. The Sylow p-decomposition may be used to obtain corresponding results for any upper class.
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Lyness, J.N. & Joe, Stephen(2003). The Number of Lattice Rules of Specified Upper Class and Rank. Bit Numerical Mathematics, 43(2), 413-426.
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Springer Netherlands