Laminated Lattices

  • J. H. Conway
  • N. J. A. Sloane
Part of the Grundlehren der mathematischen Wissenschaften book series (GL, volume 290)

Abstract

We study the densest lattice packings that can be built up in layers. Start with the 1-dimensional lattice Λl of even integer points; at the nth step stack layers of a suitable (n − 1)-dimensional lattice Λ n − 1 as densely as possible, keeping the same minimal norm; the result is a laminated lattice Λ n . In this chapter the density of Λ n is determined for n ≤ 48, all Λ n are found for n ≤ 25, and at least one Λ n is found for 26 ≤ n ≤ 48. The unique Λ24 is the Leech lattice. Denser lattices than Λ n are now known for n ≥ 30.

Keywords

Minimal Norm Integer Point Deep Hole Congruence Class Dimensional Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • J. H. Conway
  • N. J. A. Sloane

There are no affiliations available

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