Table of the Highest Kissing Numbers Presently Known

NOTE: This database has moved to Gabriele Nebe's web site in Aachen.

Please click here.

Keywords: tables, kissing number, lattices, quadratic forms, packings

Part of the Catalogue of Lattices which is a joint project of Gabriele Nebe, University of Ulm (nebe@mathematik.uni-ulm.de) and Neil J. A. Sloane, AT&T Labs-Research (njas@research.att.com).

Last modified Jul 10, 2004

Highest kissing numbers presently known in dimensions up to 128.
The entry gives the lattice with the highest kissing number known
(and if a nonlattice with a higher kissing number is known this appears in parentheses)
The kissing number in a nonlattice packing may vary from sphere to sphere -- we give the largest value.
For further details about any of the packings mentioned that don't have links, see SPLAG 3rd edition
DimKissing number for a lattice (nonlattice)Lattice (resp. nonlattice)
12LAMBDA1 = A1 = Z
26LAMBDA2 = A2
312LAMBDA3 = A3 = D3
424LAMBDA4 = D4
540LAMBDA5 = D5
672LAMBDA6 = E6
7126LAMBDA7 = E7
8240LAMBDA8 = E8
9272 (306)*LAMBDA9 ( P9a )*
10336 (500)*LAMBDA10 ( P10b )*
11438 (582)*LAMBDA11 ( P11c )*
12756 (840)*KAPPA12 = K12 (the Coxeter-Todd lattice) ( P12a )*
13918 (1130)*KAPPA13 ( P13a )*
141422 (1582)*LAMBDA14 ( P14b )*
152340 (2564)*LAMBDA15 ( P15a )*
164320LAMBDA16
175346LAMBDA17
187398LAMBDA18
1910668LAMBDA19
2017400LAMBDA20
2127720LAMBDA21
2249896LAMBDA22
2393150LAMBDA23
24196560Leech lattice LAMBDA24
25196656LAMBDA25
26196848LAMBDA26
27197142LAMBDA27
28197736LAMBDA28
29198506LAMBDA29
30200046LAMBDA30
31202692LAMBDA31
32261120 (276032)*Q32 and others (Nonlattice [EdRS98])*
33262272 (294592)*Q33 (Nonlattice [EdRS98])*
34264576 (318020)*Q34 (Nonlattice [EdRS98])*
35268032 (370892)*Q35 (Nonlattice [EdRS98])*
36274944 (438872)*Q36 (Nonlattice [EdRS98])*
37284160 (439016)*Q37 (Nonlattice [EdRS98])*
38302592 (566652)*Q38 (Nonlattice [EdRS98])*
39333696 (714184)*Q39 (Nonlattice [EdRS98])*
40399360 (991792)*Q40 (Nonlattice [EdRS98])*
42              (1196788)*      (Nonlattice [EdRS98])*
442708112 (2948552)*MW44 (Nonlattice [EdRS98])*
4852416000P48n, P48p, P48q
64138458880 (331737984)*Ne64 [Nebe98], [Nebe98b] ([EdRS98])*
801250172000 (1368532064)*L80 of Bachoc-Nebe [BacoNe98] ([EdRS98])*
128218044170240 (8863556495104)*MW128 [Elkies98] ([EdRS98])*

__________
* Nonlattice packing.

References (Other than those already given in SPLAG)


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