Lyness, J.N.Joe, Stephen2009-02-102009-02-102003Lyness, J.N. & Joe, Stephen(2003). The Number of Lattice Rules of Specified Upper Class and Rank. Bit Numerical Mathematics, 43(2), 413-426.https://hdl.handle.net/10289/2003The 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.application/pdfenThis 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.mathematicslattice rulesupper classrank of lattice rulesylow p- decompositionJournal Article10.1023/A:1026048021823