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Laminated Lattices

J. H. Conway and N. J. A. Sloane
Annals of Mathematics
Second Series, Vol. 116, No. 3 (Nov., 1982), pp. 593-620
Published by: Annals of Mathematics
DOI: 10.2307/2007025
Stable URL: http://www.jstor.org/stable/2007025
Page Count: 28
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Laminated Lattices
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Abstract

Start with the 1-dimensional lattice Λ1 of even integer points; at the n-th step stack layers of a suitable (n -)-dimensional lattice Λn - 1 as densely as possible, keeping the same minimal norm; the result is a laminated lattice Λn. In this paper the density of Λn is determined for n ⩽ 48, all δn are found for n ⩽ 25, and at least one δn if found for 26 ⩽ n ⩽ 48. The unique Λ24 is the Leech lattice. For completeness all the best sphere-packings known in dimensions up to 48 are described in the paper. A number of these are new.

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