Lattice rules by component scaling

Lyness, J. N.; Sørevik, T.

doi:10.1090/S0025-5718-1993-1185247-6

Lattice rules by component scaling
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by J. N. Lyness and T. Sørevik PDF

Math. Comp. 61 (1993), 799-820 Request permission

Abstract:

We introduce a theory of rectangular scaling of integer lattices. This may be used to construct families of lattices. We determine the relation between the Zaremba index $\rho (\Lambda )$ of various members of the same family. It appears that if one member of a family has a high index, some of the other family members of higher order may have extraordinarily high indices. We have applied a technique based on this theory to lists of good lattices available to us. This has enabled us to construct lists of excellent previously unknown lattices of high order in three and four dimensions and of moderate order in five dimensions.

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