On the Extremality of an 80-Dimensional Lattice

Damien Stehle; Mark Watkins

doi:10.1007/978-3-642-14518-6_27

On the Extremality of an 80-Dimensional Lattice

Damien Stehle, Mark Watkins

School of Computing

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

9 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 language	English
Title of host publication	Algorithmic Number Theory; Proceedings of the 9th International Symposium on Algorithmic Number Theory (ANTS-IX); Lecture Notes in Computer Science 6197
Editors	Guillaume Hanrot, Francois Morain, Emmanuel Thome
Place of Publication	Germany
Publisher	Springer, Springer Nature
Pages	340-356
Number of pages	17
ISBN (Print)	9783642145179
DOIs	https://doi.org/10.1007/978-3-642-14518-6_27
Publication status	Published - 2010
Event	The 9th International Symposium on Algorithmic Number Theory (ANTS-IX) - Nancy, France Duration: 19 Jul 2010 → 23 Jul 2010

Conference

Conference	The 9th International Symposium on Algorithmic Number Theory (ANTS-IX)
City	Nancy, France
Period	19/07/10 → 23/07/10

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10.1007/978-3-642-14518-6_27

Cite this

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title = "On the Extremality of an 80-Dimensional Lattice",

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.",

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Stehle, D & Watkins, M 2010, On the Extremality of an 80-Dimensional Lattice. in G Hanrot, F Morain & E Thome (eds), Algorithmic Number Theory; Proceedings of the 9th International Symposium on Algorithmic Number Theory (ANTS-IX); Lecture Notes in Computer Science 6197. Springer, Springer Nature, Germany, pp. 340-356, The 9th International Symposium on Algorithmic Number Theory (ANTS-IX), Nancy, France, 19/07/10. https://doi.org/10.1007/978-3-642-14518-6_27

On the Extremality of an 80-Dimensional Lattice. / Stehle, Damien; Watkins, Mark.
Algorithmic Number Theory; Proceedings of the 9th International Symposium on Algorithmic Number Theory (ANTS-IX); Lecture Notes in Computer Science 6197. ed. / Guillaume Hanrot; Francois Morain; Emmanuel Thome. Germany: Springer, Springer Nature, 2010. p. 340-356.

Research output: Chapter in Book/Report/Conference proceeding › Conference proceeding contribution › peer-review

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T1 - On the Extremality of an 80-Dimensional Lattice

AU - Stehle, Damien

AU - Watkins, Mark

PY - 2010

Y1 - 2010

N2 - 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.

AB - 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.

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DO - 10.1007/978-3-642-14518-6_27

M3 - Conference proceeding contribution

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SP - 340

EP - 356

BT - Algorithmic Number Theory; Proceedings of the 9th International Symposium on Algorithmic Number Theory (ANTS-IX); Lecture Notes in Computer Science 6197

A2 - Hanrot, Guillaume

A2 - Morain, Francois

A2 - Thome, Emmanuel

PB - Springer, Springer Nature

CY - Germany

T2 - The 9th International Symposium on Algorithmic Number Theory (ANTS-IX)

Y2 - 19 July 2010 through 23 July 2010

ER -

On the Extremality of an 80-Dimensional Lattice

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