Tables of integral unimodular lattices constructed as \(k\)-neighbors in \(\mathbb{Z}^n\) (Q1388997)

Two lattices \(L\) and \(M\) on euclidean \({\mathbb R}^n\) are said to be \(k\)-neighbors for some positive integer \(k\) if both \(L/(L\cap M)\) and \(M/(L\cap M)\) are cyclic groups of order \(k\). The integral \(k\)-neighbors of the standard lattice \({\mathbb Z}^n\) represent all classes of self-dual lattices (the proof is sketched). In the tables published here one can find such a description for any class up to \(n=24\), together with some information related to the enumeration of these lattices in [\textit{J. H. Conway} and \textit{N. J. A. Sloane}, Sphere packings, lattices and groups. 2nd ed. (1993; Zbl 0785.11036)].