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Mathematics of Computation

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Five-dimensional $ K$-optimal lattice rules

Authors: J. N. Lyness and Tor Sørevik
Journal: Math. Comp. 75 (2006), 1467-1480
MSC (2000): Primary 41A55, 41A63, 42A10; Secondary 65D32
Published electronically: March 13, 2006
MathSciNet review: 2219038
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Abstract: A major search program is described that has been used to determine a set of five-dimensional $ K$-optimal lattice rules of enhanced trigonometric degrees up to 12. The program involved a distributed search, in which approximately 190 CPU-years were shared between more than 1,400 computers in many parts of the world.

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Additional Information

J. N. Lyness
Affiliation: Mathematics and Computer Science Division, Argonne National Laboratory, 9700 South Cass Avenue, Argonne, Illinois 60439-4844 and School of Mathematics, The University of New South Wales, Sydney 2052, Australia

Tor Sørevik
Affiliation: Department of Mathematics, University of Bergen, N-5020 Bergen, Norway

Keywords: Multidimensional cubature, optimal lattice rules, $K$-optimal rules, and optimal trigonometric rules.
Received by editor(s): September 22, 2004
Received by editor(s) in revised form: April 25, 2005
Published electronically: March 13, 2006
Additional Notes: The first author’s work was supported by the Mathematical, Information, and Computational Sciences Division subprogram of the Office of Advanced Scientific Computing Research, Office of Science, U.S. Department of Energy, under Contract W-31-109-Eng-38
Article copyright: © Copyright 2006 American Mathematical Society