The Lattice KP36
An entry from the Catalogue of Lattices, which is a joint project of
Gabriele Nebe, RWTH Aachen University
(nebe@math.rwth-aachen.de)
and
Neil J. A. Sloane
(njasloane@gmail.com)
Last modified Fri Jul 18 13:17:28 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
MINIMAL_NORM
KISSING_NUMBER
DET
GRAM
PROPERTIES
NOTES
REFERENCES
LAST_LINE
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NAME
KP36
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DIMENSION
36
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MINIMAL_NORM
8
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KISSING_NUMBER
239598
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DET
3486784401
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GRAM
36 36
18 -9 3 -12 6 -12 9 -9 3 -6 9 -9 9 -6 3 -6
-3 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 3 0
-9 18 9 3 6 6 0 9 3 3 0 9 -3 9 3 3
6 -3 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 -3 3
3 9 18 -9 9 -3 0 6 9 -3 2 5 -2 7 8 -4
8 -7 3 -3 4 -2 4 -2 4 -2 4 -2 4 -2 4 -2
4 -2 -6 3
-12 3 -9 18 -6 9 -6 0 -6 9 -7 2 -5 -2 -4 8
-1 8 0 3 -2 4 -2 4 -2 4 -2 4 -2 4 -2 4
-2 4 3 -6
6 6 9 -6 14 -7 9 0 6 -3 8 2 4 4 6 -3
3 -6 0 0 -2 1 0 0 0 0 0 0 0 0 0 0
0 0 0 3
-12 6 -3 9 -7 14 -9 9 -3 6 -10 8 -8 4 -3 6
3 3 0 0 1 -2 0 0 0 0 0 0 0 0 0 0
0 0 -3 0
9 0 0 -6 9 -9 22 -11 -1 -4 16 -8 13 -5 -2 -2
-7 -1 -7 5 -7 5 -5 4 -4 2 -4 2 -4 2 -4 2
-4 2 9 0
-9 9 6 0 0 9 -11 22 5 -1 -8 16 -8 13 4 -2
8 -7 2 -7 2 -7 1 -5 2 -4 2 -4 2 -4 2 -4
2 -4 -9 9
3 3 9 -6 6 -3 -1 5 10 -5 -2 4 -3 6 6 -3
7 -5 3 -3 3 -3 3 -3 3 -3 4 -2 4 -2 4 -2
4 -2 -6 3
-6 3 -3 9 -3 6 -4 -1 -5 10 -2 -2 -3 -3 -3 6
-2 7 0 3 0 3 0 3 0 3 -2 4 -2 4 -2 4
-2 4 3 -6
9 0 2 -7 8 -10 16 -8 -2 -2 20 -10 13 -5 -2 -2
-7 -1 -6 3 -5 4 -5 4 -4 2 -5 4 -4 2 -4 2
-4 2 9 0
-9 9 5 2 2 8 -8 16 4 -2 -10 20 -8 13 4 -2
8 -7 3 -6 1 -5 1 -5 2 -4 1 -5 2 -4 2 -4
2 -4 -9 9
9 -3 -2 -5 4 -8 13 -8 -3 -3 13 -8 16 -8 -1 -4
-7 -1 -6 3 -5 4 -4 2 -5 4 -6 3 -6 3 -4 2
-4 2 9 0
-6 9 7 -2 4 4 -5 13 6 -3 -5 13 -8 16 5 -1
8 -7 3 -6 1 -5 2 -4 1 -5 3 -6 3 -6 2 -4
2 -4 -9 9
3 3 8 -4 6 -3 -2 4 6 -3 -2 4 -1 5 12 -6
6 -6 5 -4 2 -1 4 -2 4 -2 5 -4 2 -1 3 -3
4 -2 -6 3
-6 3 -4 8 -3 6 -2 -2 -3 6 -2 -2 -4 -1 -6 12
0 6 -1 5 -1 2 -2 4 -2 4 -1 5 -1 2 0 3
-2 4 3 -6
-3 6 8 -1 3 3 -7 8 7 -2 -7 8 -7 8 6 0
14 -7 4 -2 5 -4 4 -2 4 -2 4 -2 5 -4 4 -2
7 -5 -9 3
-3 -3 -7 8 -6 3 -1 -7 -5 7 -1 -7 -1 -7 -6 6
-7 14 -2 4 -1 5 -2 4 -2 4 -2 4 -1 5 -2 4
-2 7 6 -9
0 0 3 0 0 0 -7 2 3 0 -6 3 -6 3 5 -1
4 -2 8 -4 4 -2 4 -2 4 -2 4 -2 4 -2 4 -2
4 -2 -6 0
0 0 -3 3 0 0 5 -7 -3 3 3 -6 3 -6 -4 5
-2 4 -4 8 -2 4 -2 4 -2 4 -2 4 -2 4 -2 4
-2 4 6 -6
0 0 4 -2 -2 1 -7 2 3 0 -5 1 -5 1 2 -1
5 -1 4 -2 8 -4 4 -2 4 -2 4 -2 4 -2 4 -2
4 -2 -6 0
0 0 -2 4 1 -2 5 -7 -3 3 4 -5 4 -5 -1 2
-4 5 -2 4 -4 8 -2 4 -2 4 -2 4 -2 4 -2 4
-2 4 6 -6
0 0 4 -2 0 0 -5 1 3 0 -5 1 -4 2 4 -2
4 -2 4 -2 4 -2 8 -4 4 -2 4 -2 4 -2 4 -2
4 -2 -6 0
0 0 -2 4 0 0 4 -5 -3 3 4 -5 2 -4 -2 4
-2 4 -2 4 -2 4 -4 8 -2 4 -2 4 -2 4 -2 4
-2 4 6 -6
0 0 4 -2 0 0 -4 2 3 0 -4 2 -5 1 4 -2
4 -2 4 -2 4 -2 4 -2 8 -4 4 -2 4 -2 4 -2
4 -2 -6 0
0 0 -2 4 0 0 2 -4 -3 3 2 -4 4 -5 -2 4
-2 4 -2 4 -2 4 -2 4 -4 8 -2 4 -2 4 -2 4
-2 4 6 -6
0 0 4 -2 0 0 -4 2 4 -2 -5 1 -6 3 5 -1
4 -2 4 -2 4 -2 4 -2 4 -2 8 -4 4 -2 4 -2
4 -2 -6 0
0 0 -2 4 0 0 2 -4 -2 4 4 -5 3 -6 -4 5
-2 4 -2 4 -2 4 -2 4 -2 4 -4 8 -2 4 -2 4
-2 4 6 -6
0 0 4 -2 0 0 -4 2 4 -2 -4 2 -6 3 2 -1
5 -1 4 -2 4 -2 4 -2 4 -2 4 -2 8 -4 4 -2
4 -2 -6 0
0 0 -2 4 0 0 2 -4 -2 4 2 -4 3 -6 -1 2
-4 5 -2 4 -2 4 -2 4 -2 4 -2 4 -4 8 -2 4
-2 4 6 -6
0 0 4 -2 0 0 -4 2 4 -2 -4 2 -4 2 3 0
4 -2 4 -2 4 -2 4 -2 4 -2 4 -2 4 -2 8 -4
4 -2 -6 0
0 0 -2 4 0 0 2 -4 -2 4 2 -4 2 -4 -3 3
-2 4 -2 4 -2 4 -2 4 -2 4 -2 4 -2 4 -4 8
-2 4 6 -6
0 0 4 -2 0 0 -4 2 4 -2 -4 2 -4 2 4 -2
7 -2 4 -2 4 -2 4 -2 4 -2 4 -2 4 -2 4 -2
8 -4 -6 0
0 0 -2 4 0 0 2 -4 -2 4 2 -4 2 -4 -2 4
-5 7 -2 4 -2 4 -2 4 -2 4 -2 4 -2 4 -2 4
-4 8 6 -6
3 -3 -6 3 0 -3 9 -9 -6 3 9 -9 9 -9 -6 3
-9 6 -6 6 -6 6 -6 6 -6 6 -6 6 -6 6 -6 6
-6 6 12 -6
0 3 3 -6 3 0 0 9 3 -6 0 9 0 9 3 -6
3 -9 0 -6 0 -6 0 -6 0 -6 0 -6 0 -6 0 -6
0 -6 -6 12
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PROPERTIES
INTEGRAL =1
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NOTES
The Kschischang-Pasupathy 36-d lattice, the densest packing known in 36 dimensions.
Sent by Christine Bachoc <bachoc@math.u-bordeaux.fr> .
math.u-bordeaux.fr!bachoc Wed Sep 4 11:05:44 +0200 1996
A Gram matrix of the lattice of dim 36 det 3^20 min 8
constructed over the Eisensteins.
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REFERENCES
PGIT March 1992 vol 38 p. 227.
SPLAG Second edition page xvi.
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LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe