Constructions of some perfect integral lattices with minimum 4
Journal de Théorie des Nombres de Bordeaux, Volume 27 (2015) no. 3, pp. 655-687.

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

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

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

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

[1] N. D. Elkies, « Answer to Mathoverflow question: A curious identity related to finite fields », .

[2] J. Martinet, Les réseaux parfaits des espaces euclidiens, Mathématiques. [Mathematics], Masson, Paris, 1996, iv+439 pages. | MR: 1434803 | Zbl: 0869.11056

[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: 1957723

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