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

Published online by Cambridge University Press:  26 February 2010

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

Type
Research Article
Copyright
Copyright © University College London 1993

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