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On the extremality of an 80-dimensional lattice

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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. © 2010 Springer-Verlag Berlin Heidelberg.




Stehlé, D., & Watkins, M. (2010). On the extremality of an 80-dimensional lattice. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6197 LNCS, pp. 340–356).

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