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.