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The existence of efficient lattice rules for multidimensional numerical integration


Author: Harald Niederreiter
Journal: Math. Comp. 58 (1992), 305-314, S7
MSC: Primary 65D30; Secondary 11K45
DOI: https://doi.org/10.1090/S0025-5718-1992-1106976-5
MathSciNet review: 1106976
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Abstract: In this contribution to the theory of lattice rules for multidimensional numerical integration, we first establish bounds for various efficiency measures which lead to the conclusion that in the search for efficient lattice rules one should concentrate on lattice rules with large first invariant. Then we prove an existence theorem for efficient lattice rules of rank 2 with prescribed invariants, which extends an earlier result of the author for lattice rules of rank 1.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1992-1106976-5
Article copyright: © Copyright 1992 American Mathematical Society

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