On the Extremality of an 80-Dimensional Lattice

Damien Stehle, Mark Watkins

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contribution

6 Citations (Scopus)

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 �-series, along with fast vector enumeration techniques including pruning, while also using the automorphisms of the lattice.
Original languageEnglish
Title of host publicationAlgorithmic Number Theory; Proceedings of the 9th International Symposium on Algorithmic Number Theory (ANTS-IX); Lecture Notes in Computer Science 6197
EditorsGuillaume Hanrot, Francois Morain, Emmanuel Thome
Place of PublicationGermany
PublisherSpringer, Springer Nature
Pages340-356
Number of pages17
ISBN (Print)9783642145179
DOIs
Publication statusPublished - 2010
EventThe 9th International Symposium on Algorithmic Number Theory (ANTS-IX) - Nancy, France
Duration: 19 Jul 201023 Jul 2010

Conference

ConferenceThe 9th International Symposium on Algorithmic Number Theory (ANTS-IX)
CityNancy, France
Period19/07/1023/07/10

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