The Lattice L37
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 13:27:44 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
BASIS
GRAM
MINIMUM
KISSING_NUMBER
PROPERTIES
NOTES
LAST_LINE
-
NAME
L37
-
DIMENSION
37
-
DET
1
-
BASIS
37 37
0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0
0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 0 0
0 0 0 0 0 0 -2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 2 2 0 0 0
0 -1 1 0 0 0 1 -1 0 -1 -1 0 1 0 -1 -1 0 0 0 -1 1 1 1 1 1 0 0 0 0 -1 1 0 -1 0 1
0 1
1 0 0 0 0 0 0 1 0 1 0 0 1 0 -1 0 1 1 0 0 1 1 1 1 0 0 0 0 0 1 1 0 -2 1 1 0 1
0 0 0 1 0 0 0 0 0 0 0 0 1 1 -1 0 0 0 1 1 0 0 1 1 1 1 0 1 1 0 0 0 1 1 0 1 1
-1 0 0 0 1 0 -1 0 1 -1 0 1 0 1 0 1 0 0 1 0 0 -1 0 -1 0 0 0 0 0 1 -1 0 0 -1 0 -1
1
0 0 0 0 0 1 -1 0 0 1 1 1 0 0 1 0 0 0 0 1 1 1 1 1 1 1 1 1 0 0 0 2 0 0 0 -1 0
0 1 0 0 0 0 0 -1 1 1 1 0 0 1 1 1 0 1 0 1 0 0 0 0 0 1 1 0 1 -1 0 1 0 1 0 0 0
0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 0 0 0 2 0 0
0 0 0 0 0 0 0 -2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2
-1 0 1 0 0 0 1 -1 -1 1 0 0 0 -1 -1 0 -1 0 0 0 0 0 0 0 1 1 1 0 1 -1 0 1 1 0 0 0
0
0 0 0 0 0 0 0 -2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 0 0 2
0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
0 0 0 0 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 -2 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 0 2 2 0 0 0
0 0 0 0 0 0 0 0 0 -2 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 0 0 2 0
0 0 0 0 0 -1 -1 -2 0 -1 1 -1 0 0 1 0 0 0 0 -1 -1 -1 -1 -1 -1 -1 -1 -1 0 0 0 0 0
0 0 -1 0
0 0 0 0 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 0 2 0
1 0 -1 0 0 0 -1 -1 -1 1 0 0 0 -1 -1 0 1 0 0 0 0 0 0 0 -1 -1 -1 0 -1 -1 0 -1 -1
0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0
-1 -1 1 0 0 0 -1 0 0 0 -1 0 0 0 0 -1 1 -1 0 -1 0 0 0 0 1 0 0 0 0 0 0 0 -1 1 2 0
0
-1 0 0 0 0 0 0 1 0 -1 0 0 1 0 1 0 -1 1 0 0 -1 -1 -1 -1 0 0 0 0 0 1 -1 0 2 1 1 0
-1
0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0
0 0 0 0 0 0 0 2 0 2 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 -2 0 0 0 0 0
0 0 0 0 -2 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -2 0 0 0 0 0 0 0
0 0 0 0 0 0 -2 0 0 0 0 0 0 2 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 -2 2 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 -2 0 0 0 0 0 -2 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 -2 -2 2 0 0 0
0 0 0 0 0 0 0 0 0 -2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 -2 0 0 0
0 -1 0 0 0 0 0 -1 -1 -1 -1 0 0 1 -1 -1 0 -1 0 -1 0 0 0 0 0 -1 -1 0 1 -1 0 -1 0
-1 0 0 0
1 -1 -1 0 0 0 1 0 0 0 1 0 0 0 0 -1 -1 -1 0 1 0 0 0 0 1 0 0 0 0 0 0 2 1 -1 0 -2
0
1 0 -1 0 0 0 1 1 1 1 0 0 0 1 -1 0 1 0 0 0 0 0 0 0 -1 1 -1 0 1 1 0 -1 1 0 0 0 0
0 0 1 -1 0 0 1 0 1 0 0 0 0 0 -1 0 0 1 -1 -1 1 1 0 0 0 0 1 1 0 2 1 1 -2 0 1 -1
0
-
GRAM
37 37
3 0 -1 1 0 -1 1 -1 -1 0 0 0 1 1 1 -1 1 1 -1 -1 -1 1 -1 1 0 0 0 0 -1 0 0 -1 0 0
0 1 -1
0 3 0 0 0 1 0 0 1 0 1 -1 0 -1 0 0 0 -1 -1 0 -1 0 1 1 1 1 -1 -1 0 0 0 -1 0 -1 1
0 1
-1 0 3 1 -1 0 0 0 1 1 0 0 -1 1 0 1 1 0 1 1 0 0 1 1 0 0 -1 0 1 1 -1 1 -1 -1 -1
-1 -1
1 0 1 3 -1 0 1 0 0 0 -1 0 0 2 1 1 1 0 0 -1 -1 1 0 2 0 0 0 -1 0 0 0 0 -1 -1 0 1
0
0 0 -1 -1 5 2 1 -1 0 -1 1 1 1 1 -1 -1 0 1 -1 0 0 0 2 -2 0 -1 1 1 -1 0 1 1 1 2 0
-1 2
-1 1 0 0 2 5 1 -1 1 0 0 0 -1 0 -1 -1 -1 0 -2 1 1 -1 1 -2 0 1 1 -1 0 0 1 2 -1 -1
-1 1 3
1 0 0 1 1 1 4 0 1 1 0 1 1 2 0 0 1 1 -2 0 -1 0 0 0 1 0 1 0 1 -1 1 0 0 0 0 1 -1
-1 0 0 0 -1 -1 0 4 0 0 0 1 -1 0 0 1 -1 0 1 0 -1 -1 0 1 1 0 0 -1 1 -1 -1 -1 1 0
0 0 0
-1 1 1 0 0 1 1 0 5 2 0 0 1 0 0 1 0 -2 -2 0 -1 0 0 -1 1 1 -1 0 1 1 0 -1 0 -2 2
-1 1
0 0 1 0 -1 0 1 0 2 4 1 1 1 1 0 0 1 -1 0 0 -1 -1 -1 0 1 0 -1 1 1 0 -1 0 -1 -2 0
0 0
0 1 0 -1 1 0 0 0 0 1 3 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 0 1 0 0 -1 0 0 0 0 0 0
0 -1 0 0 1 0 1 1 0 1 0 3 0 2 -1 0 0 0 1 0 0 -1 0 -1 1 -1 0 1 1 -1 0 0 0 1 0 0
0
1 0 -1 0 1 -1 1 -1 1 1 0 0 4 1 1 0 1 -1 -1 -1 -1 1 0 0 0 0 0 1 -1 0 1 -1 0 0 1
-1 0
1 -1 1 2 1 0 2 0 0 1 0 2 1 5 1 1 2 1 1 -1 0 1 0 1 0 -1 0 1 0 0 0 0 -1 0 0 0 -1
1 0 0 1 -1 -1 0 0 0 0 0 -1 1 1 3 1 1 0 0 -1 0 1 -1 1 -1 0 0 0 -1 1 0 -1 0 -1 0
0 -1
-1 0 1 1 -1 -1 0 1 1 0 0 0 0 1 1 3 1 -1 1 -1 0 1 0 1 0 0 0 0 1 0 0 -1 0 0 1 0
-1
1 0 1 1 0 -1 1 -1 0 1 1 0 1 2 1 1 3 0 0 -1 0 1 0 1 0 0 0 1 0 0 0 0 -1 0 0 0 -2
1 -1 0 0 1 0 1 0 -2 -1 0 0 -1 1 0 -1 0 4 0 1 0 0 0 1 -1 -1 1 0 0 0 0 1 1 1 -2 0
-1
-1 -1 1 0 -1 -2 -2 1 -2 0 0 1 -1 1 0 1 0 0 5 0 1 0 0 1 0 -2 -1 1 0 0 -1 0 0 1 0
-1 -1
-1 0 1 -1 0 1 0 0 0 0 0 0 -1 -1 -1 -1 -1 1 0 3 1 -1 1 -1 0 0 0 0 1 0 0 1 0 0 -2
-1 0
-1 -1 0 -1 0 1 -1 -1 -1 -1 0 0 -1 0 0 0 0 0 1 1 4 0 0 -2 -1 0 1 1 0 0 1 1 -1 1
-1 0 -1
1 0 0 1 0 -1 0 -1 0 -1 0 -1 1 1 1 1 1 0 0 -1 0 3 0 1 -1 0 0 0 -1 1 0 -1 0 0 1 0
-1
-1 1 1 0 2 1 0 0 0 -1 1 0 0 0 -1 0 0 0 0 1 0 0 4 0 0 0 0 0 0 0 0 1 0 1 -1 -1 1
1 1 1 2 -2 -2 0 1 -1 0 0 -1 0 1 1 1 1 1 1 -1 -2 1 0 5 0 0 -1 -1 0 0 -1 -1 0 -1
0 0 -1
0 1 0 0 0 0 1 1 1 1 0 1 0 0 -1 0 0 -1 0 0 -1 -1 0 0 3 0 -1 0 1 -1 0 -1 0 0 1 0
0
0 1 0 0 -1 1 0 0 1 0 0 -1 0 -1 0 0 0 -1 -2 0 0 0 0 0 0 3 0 -1 0 0 0 0 -1 -1 0 1
0
0 -1 -1 0 1 1 1 0 -1 -1 0 0 0 0 0 0 0 1 -1 0 1 0 0 -1 -1 0 3 0 0 -1 1 1 0 1 -1
1 0
0 -1 0 -1 1 -1 0 -1 0 1 1 1 1 1 0 0 1 0 1 0 1 0 0 -1 0 -1 0 3 0 0 0 0 0 1 0 -1
-1
-1 0 1 0 -1 0 1 1 1 1 0 1 -1 0 -1 1 0 0 0 1 0 -1 0 0 1 0 0 0 3 -1 0 0 0 0 0 0
-1
0 0 1 0 0 0 -1 -1 1 0 0 -1 0 0 1 0 0 0 0 0 0 1 0 0 -1 0 -1 0 -1 3 -1 0 0 -1 0
-1 0
0 0 -1 0 1 1 1 -1 0 -1 -1 0 1 0 0 0 0 0 -1 0 1 0 0 -1 0 0 1 0 0 -1 3 0 0 1 0 0
0
-1 -1 1 0 1 2 0 -1 -1 0 0 0 -1 0 -1 -1 0 1 0 1 1 -1 1 -1 -1 0 1 0 0 0 0 4 -1 0
-2 0 1
0 0 -1 -1 1 -1 0 1 0 -1 0 0 0 -1 0 0 -1 1 0 0 -1 0 0 0 0 -1 0 0 0 0 0 -1 3 1 1
-1 0
0 -1 -1 -1 2 -1 0 0 -2 -2 0 1 0 0 -1 0 0 1 1 0 1 0 1 -1 0 -1 1 1 0 -1 1 0 1 4 0
0 -1
0 1 -1 0 0 -1 0 0 2 0 0 0 1 0 0 1 0 -2 0 -2 -1 1 -1 0 1 0 -1 0 0 0 0 -2 1 0 5 0
0
1 0 -1 1 -1 1 1 0 -1 0 0 0 -1 0 0 0 0 0 -1 -1 0 0 -1 0 0 1 1 -1 0 -1 0 0 -1 0 0
4 0
-1 1 -1 0 2 3 -1 0 1 0 0 0 0 -1 -1 -1 -2 -1 -1 0 -1 -1 1 -1 0 0 0 -1 -1 0 0 1 0
-1 0 0 6
-
MINIMUM
3
-
KISSING_NUMBER
1184
-
PROPERTIES
Unimodular = 1
-
NOTES
Constructed by Masaaki Harada from an extremal code modulo 4
Unimodular lattice with long shadow as investigated by Venkov and Nebe
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe