1. 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 8-dimensional lattices.
• Eutactic and semi-eutactic perfect, $8$-dimensional lattices, after Cordian RIENER , "On extreme forms in dimension 8", J. Th. Nombres Bordeaux 18 (2006), 677-682. dvi , postscript , pdf .
• Numerical data for the paper above: read_me , eutax8 .



2. Tables and GP-access.

• Perfect lattices in dimensions 2 to 7 : Gram matrices after Conway and Sloane; pn[i] gives P_n^i.
• gp-access to 7-dimensional perfect LLL-reduced lattices.
• gp-access to 8-dimensional perfect Laihem lattices.
• gp-access to 8-dimensional perfect Baril lattices.
• gp-access to 8-dimensional perfect Napias lattices.
• gp-access to 8-dimensional perfect Batut lattices.



3. Tables of 8-dimensional perfect lattices in PARI-GP format.
   These tables are to be loaded, and then read by gp together with the corresponding access files.

• Table for the Laihem lattices : 1175 lattices.
• Table for the Baril lattices. : 53 lattices.
• First table for the Napias lattices : 1000 lattices.
• Second table for the Napias lattices : 1000 lattices.
• Third table for the Napias lattices : 1000 lattices.
• Fourth table for the Napias lattices : 1000 lattices.
• Fifth table for the Napias lattices : 1000 lattices.
• Sixth table for the Napias lattices : 1000 lattices.
• Seventh table for the Napias lattices : 1000 lattices.
• Eighth table for the Napias lattices : 1000 lattices.
• Ninth table for the Napias lattices : 1000 lattices.
• Tenth table for the Napias lattices :   542 lattices.
• Table for the Batut lattices : 146 lattices.



4. Tables of various (very often perfect) lattices in PARI-GP format. (Nov. 2004)
   These tables can be loaded under PARI-GP; the comments can be read with an editor.

• Some Lattices contained in the Leech lattice : Lattices Lambda_n, K_n, K'_n, Plesken-Pohst for minimum 4, ...
• Antilaminations of O_{23}.
• Plesken-Pohst lattices of minimum 3.
• Some Integral Lattices of Minimum 6.



5. Voronoi graphs in dimensions 2 to 7; minimal classes in dimensions 2 to 4. (Dec. 2004)
   The three PARI-GP files can be loaded under PARI-GP; the comments can be read with an editor (e.g., emacs).



• Voronoi graphs and minimal classes. dvi , postscript , pdf .
• The Voronoi graphs in dimensions 2 to 6.
• The Voronoi graph in dimension 7.
• Minimal classes in dimensions 2 to 4.



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



• Lattices and spherical designs. dvi , postscript , pdf .
• Strongly (semi-)eutactic lattices (dimensions 2 to 6: complete; 7,8,9,10: examples).
• Known strongly perfect lattices in dimensions 2 to 26.
  This list in dimensions up to 24 is that of Venkov's original paper published in L'Enseignement Mathématique in 2001. At the date of January 1st, 2011, no new lattice in these dimensions had been found.



7. Varia

• Some lattices of Roland Bacher (Nov. 28th, 2008) after Invent. Math. 130 (1997), 153--158.
• Lattices in dimensions 28 to 22.)
• Unimodular lattices of minimum 3 in dimensions 23 to 28 (May 14th, 2010) after Bacher and Venkov.
• User's guide dvi , postscript , pdf .
• GP-file

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