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

Received: 2014-02-18
Revised: 2015-09-07
Accepted: 2015-10-01
Published online: 2016-01-11
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
Author's affiliations:

@article{JTNB_2015__27_3_655_0,
     author = {Roland Bacher},
     title = {Constructions of some perfect integral lattices with minimum $4$},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {655--687},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {27},
     number = {3},
     year = {2015},
     doi = {10.5802/jtnb.918},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.918/}
}

TY  - JOUR
TI  - Constructions of some perfect integral lattices with minimum $4$
JO  - Journal de Théorie des Nombres de Bordeaux
PY  - 2015
DA  - 2015///
SP  - 655
EP  - 687
VL  - 27
IS  - 3
PB  - Société Arithmétique de Bordeaux
UR  - https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.918/
UR  - https://doi.org/10.5802/jtnb.918
DO  - 10.5802/jtnb.918
LA  - en
ID  - JTNB_2015__27_3_655_0
ER  - 

%0 Journal Article
%T Constructions of some perfect integral lattices with minimum $4$
%J Journal de Théorie des Nombres de Bordeaux
%D 2015
%P 655-687
%V 27
%N 3
%I Société Arithmétique de Bordeaux
%U https://doi.org/10.5802/jtnb.918
%R 10.5802/jtnb.918
%G en
%F JTNB_2015__27_3_655_0

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/