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On the Extremality of an 80-Dimensional Lattice

  • Damien Stehlé
  • Mark Watkins
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6197)

Abstract

We show that a specific even unimodular lattice of dimension 80, first investigated by Schulze-Pillot and others, is extremal (i.e., the minimal nonzero norm is 8). This is the third known extremal lattice in this dimension. The known part of its automorphism group is isomorphic to SL 2(F 79), which is smaller (in cardinality) than the two previous examples. The technique to show extremality involves using the positivity of the Θ-series, along with fast vector enumeration techniques including pruning, while also using the automorphisms of the lattice.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Damien Stehlé
    • 1
    • 2
  • Mark Watkins
    • 2
  1. 1.CNRS and Macquarie University 
  2. 2.Magma Computer Algebra Group, School of Mathematics and StatisticsUniversity of SydneyAustralia

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