Construction of some perfect integral lattices with minimum 4

Roland Bacher (1)

1 IF - Institut Fourier

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 $k$.

Mots clés: Perfect lattice; finite abelian group; projective plane; equiangular system; Schläfli graph; Sidon set; Craig lattice

Domaines: Combinatoire [math.CO]; Théorie des nombres [math.NT]

Roland Bacher. Construction of some perfect integral lattices with minimum 4. Journal de Théorie des Nombres de Bordeaux, 2015, 27 (3). ⟨hal-00931612v2⟩