Unimodular Hunting II

By Bill Allombert and Gaëtan Chenevier
28/05/2025

This website is a companion to the paper Unimodular Hunting II by the authors.

In this paper, we classify the unimodular integral euclidean lattices of rank 28, as well as unimodular lattices of rank 29 without nonzero elements of norm <=2.
There are respectively 374062 and 10092 such lattices up to isometry.


  • (29/09/20) A list of the 29-dimensional unimodular lattices without nonzero vectors of norm <=2, given in neighbor forms.
    An associated gp scripts file, including an automatized proof that this list is complete (tutorial).
    Lists of Gram matrices of all unimodular integral lattices of rank <=29 without nonzero vectors of norm <=2: dim23, dim24, dim26, dim27, dim28, dim29 (gzipped, 3.2 MB).
    See here for the format of these lists of Gram matrices.


  • (13/11/20) A list (3.2 MB gzipped) of these 28-dimensional unimodular lattices with no norm 1 vectors, given in neighbor form (see this notice).
    The same list unzipped and split as explained in the notice: i1, i2, i3, i4, i5, i6, i7, i8, i9, i10, i11, i12, i13, i14, i15, i16, i17, i18, i19, i20, i21, i24, i28.
    An associated gp scripts file, including an automatized proof that our list is complete (tutorial).
    Gram matrices (gzipped, 95.9 MB) of all unimodular integral lattices of rank 28 without norm 1 vectors (format).