A catalogue of Perfect Lattices (Prepared jointly with C. Batut)
(Maintained by the second author alone since September 2010.)
See also
A Catalogue of Lattices ,
written by Gabriele Nebe and Neil Sloane.

About perfect lattices.
(The second file is a text file.)

Perfection: An introductory paper about perfect lattices.
dvi ,
postscript ,
pdf .

Statistics in dimension 8
: Statistics on perfect 8dimensional lattices.

Eutactic and semieutactic perfect, $8$dimensional lattices,
after Cordian RIENER ,
"On extreme forms in dimension 8",
J. Th. Nombres Bordeaux 18 (2006), 677682.
dvi ,
postscript ,
pdf .

Numerical data for the paper above:
read_me ,
eutax8 .

Dimensions 2 to 7.
All lattices are extreme except four:
P_6^4 and P_7^{26}, semieutactic; P_7^{18}, P_7^{29}, only weakly eutactic.

Dimensions 2 to 8: perfect and dualextreme lattices.
Textfile (dualextremeperf.txt)

Tables on perfect lattices in dimensions 2 to 8.
Two global tables for the 10916 perfect,
8dimensional lattices, following one table
for dimensions 2 to 7.
Next the
correspondence between the notation above and the old notation
[1175 Laihem lattices lh(i), 53 Baril lattices bari(i),
9542 Napias lattices nap(i), and 146 Batut lattices batu(i)],
both for perfection and eutaxy properties.

The file contains 6 vectors new2oldp8d{k},
k=2,...,7;
new2oldp8d{k}[i] is a 2component vector [m,j], m=1,2,3,4, and we have
p8d{k}[i]=lh(j) if m=1, bari(j) if m=2, nap(j) if m=3, batu(j) if m=4.

The file contains 4 vectors ,
old2newlh, bari, nap, batu, of 2components vectors [m,j], m=2,...,7,
and, say, if old2newnap[i]=[k,j], then p8d{k}[j]=nap(i).

For the sake of generality we depart from Riener's notation: 0 means
for not weakly eutactic (though 0 does not occur for perfect lattices),
1 means weakly eutactic but not semieutactic, 2 means semieutactic
but not eutactic, and 3 means eutactic. The file
contains six files eutp8d{k} ; eutp8d{k}[i] (=1, 2, or 3) gives
the eutactic character of p8d{k}[i].

Tables of various (very often perfect) lattices in PARIGP format.
(Creation: Nov. 2004.)
These tables can be loaded under PARIGP;
the comments can be read with any editor.

Voronoi graphs in dimensions 2 to 7; minimal classes in dimensions 2 to 4.
(Dec. 2004; modif. Nov. 11th, 2013;
files on minimal classes expanded from January 16th, 2017 onwards).
The three PARIGP files can be downloaded under PARIGP;
the comments can be read with an editor (e.g., emacs).

Strongly eutactic and strongly perfect lattices.
The two PARIGP files can be loaded under PARIGP;
the comments can be read with an editor (e.g., emacs).

Varia

Some lattices of Roland Bacher
(Nov. 28th, 2008)
after Invent. Math. 130 (1997), 153158:
Lattices in dimensions 28 to 25.

Unimodular lattices of minimum 3 in dimensions 23 to 28
(May 14th, 2010)
after Bacher and Venkov (plus two higher dimensional examples):
User's guide
dvi ,
postscript ,
pdf ;
GPfile.
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