Constructions of some perfect integral lattices with minimum 4
Bacher, Roland1
1 Univ. Grenoble Alpes, Institut Fourier 621 Avenue Centrale 38041 Saint-Martin-d’Hères FRANCE
Journal de théorie des nombres de Bordeaux, Tome 27 (2015) no. 3, pp. 655-687.

Cet article présente des constructions de plusieurs familles de sous-réseaux parfaits de ℤd avec minimum 4. En particulier, le nombre de tels réseaux parfaits de dimension d croît plus vite que tout polynôme en d.

We construct several families of perfect sublattices with minimum 4 of ℤd. In particular, the number of d-dimensional perfect integral lattices with minimum 4 grows faster than dk for every exponent k.

DOI : 10.5802/jtnb.918
Classification : 11H55, 11T06, 20K01, 05B30, 05E30
Mots-clés : Perfect lattice, finite abelian group, projective plane, equiangular system, Schläfli graph, Sidon set, Craig lattice
Bacher, Roland 1

1 Univ. Grenoble Alpes, Institut Fourier 621 Avenue Centrale 38041 Saint-Martin-d’Hères FRANCE 
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Bacher, Roland. Constructions of some perfect integral lattices with minimum $4$. Journal de théorie des nombres de Bordeaux, Tome 27 (2015) no. 3, pp. 655-687. doi : 10.5802/jtnb.918. https://www.numdam.org/articles/10.5802/jtnb.918/

[1] N. D. Elkies, « Answer to Mathoverflow question: A curious identity related to finite fields », http://mathoverflow.net/questions/158769.

[2] J. Martinet, Les réseaux parfaits des espaces euclidiens, Mathématiques. [Mathematics], Masson, Paris, 1996, iv+439 pages. | MR | Zbl

[3] —, Perfect lattices in Euclidean spaces, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 327, Springer-Verlag, Berlin, 2003, xxii+523 pages. | MR

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