Unimodular Hunting II

By Bill Allombert and Gaëtan Chenevier

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

It includes a database of all of our lattices, as well as some PARI/GP scripts to play with those lists and check that they are complete.

(13/11/20) The rank 28 unimodular lattices

A list (3.2 MB gzipped) of the 374062 rank 28 unimodular lattices with no norm 1 vectors, given in neighbor form (readme).

The same list (partially unzipped) split according to the "index" (see the readme):
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).

A list of Gram matrices of the 374062 rank 28 unimodular lattices with no norm 1 vectors (WARNING gzipped 95.9 MB, format).

A list of neighbor forms for the rank 28 unimodular lattices having norm 1 vectors, or equivalently, for all unimodular lattices of rank <28 having no norm 1 vectors, is avalable here.

(14/07/2020) The rank 29 unimodular lattices with no nonzero vectors of norm ≤ 2

A list of the 10092 rank 29 unimodular lattices without nonzero vectors of norm ≤ 2, given in neighbor forms (readme).
This file contains as well a list of all rank <29 unimodular lattices without nonzero vectors of norm ≤ 2.

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.