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 of perfect lattices of dimension .

   NEW: two global tables for the 10916 perfect, 8-dimensional lattices
• Perfect lattices in dimensions 2 to 7 : Gram matrices after Conway and Sloane; pn[i] gives P_n^i.
• The 10916 eight-dimensional perfect lattices,
  ordered by decreasing Hermite invariants. The natural, 1.6 Mega table,
  then a compressed, 0.4 Mega table; (uncompress using gunzip)
• Six sub-tables with perfect sections having the same minimum (7 to 2)
  The natural, 1.6 Mega table, then a compressed, 0.4 Mega table;
  (1175+54+4889+33+4760+5=10916 lattices)



3. 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.



4. 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.



5. 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 constructed by Batut and Venkov and published in "L'Enseignement Mathématique" in 2001. At the date of April 1st, 2012, no new lattice in these dimensions had been found.



6. Varia

• Some lattices of Roland Bacher (Nov. 28th, 2008) after Invent. Math. 130 (1997), 153--158.
• Lattices in dimensions 28 to 26. Updated on June 16th, 2013.
• 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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