Optimality and uniqueness of the Leech lattice among lattices

We prove that the Leech lattice is the unique densest lattice in R^24. The proof combines human reasoning with computer verification of the properties of certain explicit polynomials. We furthermore prove that no sphere packing in R^24 can exceed the Leech lattice's density by a factor of more than 1+1.65*10^(-30), and we give a new proof that E_8 is the unique densest lattice in R^8.

• Publication year

  2004

• Venue

  arXiv: Metric Geometry

• Publication date

  2004-03-16

• Fields of study

  Mathematics

• Identifiers
  DOI 10.4007/annals.2009.170.1003arXiv math/0403263
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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