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A bound, and a conjecture, on the maximum lattice-packing density of a superball

Part of: Geometry of numbers

Published online by Cambridge University Press:  26 February 2010

J. A. Rush
J. A. Rush
Affiliation:
Department of Mathematics, GN-50, University of Washington, Seattle, WA 98195, U.S.A..
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Abstract

We obtain explicit lower bounds on the lattice packing densities δL of superballs G of quite a general nature, and we conjecture that as the dimension n approaches infinity, the bounds are asymptotically exact. If the conjecture were true, it would follow that the maximum lattice-packing density of the Iσ-ball is 2−n(1+σ(1)) for each σ in the interval 1 ≤ σ ≤ 2.

MSC classification

Secondary: 11H31: Lattice packing and covering
Type
Research Article
Information
Mathematika , Volume 40 , Issue 1 , June 1993 , pp. 137 - 143
Copyright
Copyright © University College London 1993

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