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The Number of Lattice Rules of Specified Upper Class and Rank |
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| Authors: | J N Lyness S Joe |
| Institution: | (1) Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, IL, 60439, U.S.A.;(2) School of Mathematics, University of New South Wales, Sydney, NSW, 2052, Australia;(3) Department of Mathematics, The University of Waikato, Private Bag 3105, Hamilton, New Zealand |
| 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. |
| Keywords: | Lattice rules upper class rank of lattice rule Sylow p-decomposition |
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