On the Extremality of an 80-Dimensional Lattice

Damien Stehlé and Mark Watkins

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 SL2(F79), which is smaller (in cardinality) than the two previous examples. The technique to show extremality involves using the positivity of the Theta-series, along with fast vector enumeration techniques including pruning, while also using the automorphisms of the lattice.

Download: pdf.
Homepage