Algebraic Constructions for Lattices

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


In this chapter we construct dense lattice packings in dimensions 32, 36, 40, 48, 64, 96, ..., 65536, ... using a variety of techniques. The main constructions used are Constructions Af (a more abstract version of Construction A), D (which uses a nested family of codes) and E (a powerful general construction which can be applied recursively). Other methods construct dense lattices from ideals in algebraic number fields. We also construct E 8 and the Leech lattice using icosians.


Minimal Norm Center Density Symmetric Bilinear Form Theta Series Algebraic Number Theory 
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Copyright information

© Springer Science+Business Media New York 1988

Authors and Affiliations

  • J. H. Conway
  • N. J. A. Sloane

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