The Lattice L41
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 13:27:47 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
BASIS
GRAM
MINIMUM
KISSING_NUMBER
NOTES
LAST_LINE
-
NAME
L41
-
DIMENSION
41
-
DET
1
-
BASIS
41 41
1 0 0 0 0 0 0 0 0 0 1 0 0 1 1 0 1 0 1 1 0 1 0 1 0 0 1 0 0 1 1 0 1 1 3 1 0 1 3 3
1
0 1 0 0 0 0 0 0 0 0 1 0 1 1 1 1 1 1 0 0 1 0 0 1 1 1 1 0 0 0 1 2 2 1 0 0 3 3 3 3
1
0 0 1 0 0 0 0 0 0 0 1 1 0 0 1 1 0 0 0 1 0 0 0 1 1 1 1 0 0 0 0 3 3 0 1 0 0 2 3 3
1
0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 1 1 1 1 0 0 1 1 1 0 1 0 0 1 2 3 0 1 0 0 3 1 2
1
0 0 0 0 1 0 0 0 0 0 0 0 1 1 1 1 1 0 0 1 1 1 1 0 1 1 1 0 1 0 0 2 2 0 3 2 2 2 0 3
2
0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 1 0 1 1 1 1 1 0 1 0 0 0 1 1 1 1 0 2 3 3 3 3 3 1
0
0 0 0 0 0 0 1 0 0 0 1 0 1 1 1 1 1 1 1 1 1 0 0 1 0 1 0 1 1 0 1 1 2 0 1 3 1 0 2 2
0
0 0 0 0 0 0 0 1 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1 0 1 0 1 0 0 1 3 1 2 2 1 1 3 2 1
3
0 0 0 0 0 0 0 0 1 0 1 0 0 0 0 1 0 1 0 1 1 0 1 1 0 0 1 0 0 1 0 0 1 3 0 1 1 2 3 3
2
0 0 0 0 0 0 0 0 0 1 1 1 1 0 1 1 0 0 1 1 0 1 1 1 1 0 1 1 1 1 0 1 1 3 2 1 1 3 0 3
1
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 2 2 2 0 2 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 0 0 0 0 0 0 0 2 2 0 2 2 2 2 0 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 0 0 0 0 2 2 0 2 0 2 2 0 0
2
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 2 0 0 0 2 2 2 2 2
2
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 2 0 0 0 0 0 2 2 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 0 0 0 0 0 2 2 2 0 0 0 2 0 2
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 2 0 0 2 2 0 2 2 0
2
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 2 2 0 0 0 0 2 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 2 2 2 0 2 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 0 0 0 0 0 0 0 0 2 2 2 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 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 2 2
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 0 0 0 2 2 0 2 2 2 2 2
2
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 0 0 0 2 0 0 0 2 2 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 2 0 0 0 0 0 0 0 0 2 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 2 0 0 0 0 0 0 0 2 2 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 2 0 0 0 0 0 0 0 2 2 0 0 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 2 0 0 0 0 0 0 2 0 2 2 0 2 2
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 2 0 0 0 0 2 0 2 0 0 0 0 2
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 2 0 0 0 2 2 0 0 2 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 2 0 0 2 2 2 2 0 2 2 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 2 0 2 2 0 2 0 2 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 4 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 4 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 4 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 4 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 4 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 4 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 4 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 4 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 4
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
4
-
GRAM
41 41
11 8 8 6 8 9 7 7 8 8 5 5 3 5 4 3 5 3 2 3 3 6 4 3 4 4 5 4 3 7 4 0 1 1 3 1 0 1 3
3 1
8 15 11 9 10 10 8 10 10 9 5 7 6 8 6 6 5 5 4 2 5 8 5 5 5 3 6 3 6 6 5 2 2 1 0 0 3
3 3 3 1
8 11 13 9 9 7 7 9 8 8 5 7 5 6 6 6 5 5 3 1 3 6 4 4 4 3 4 4 4 6 4 3 3 0 1 0 0 2 3
3 1
6 9 9 10 8 6 6 8 6 7 4 6 5 5 4 5 4 4 3 1 2 5 3 3 3 2 2 4 4 5 4 2 3 0 1 0 0 3 1
2 1
8 10 9 8 14 10 8 9 7 10 6 9 7 7 4 5 6 3 4 4 3 7 3 3 4 3 5 5 5 6 3 2 2 0 3 2 2 2
0 3 2
9 10 7 6 10 16 8 9 9 10 7 7 5 7 4 4 7 3 5 6 4 8 5 3 6 4 6 2 5 8 6 1 0 2 3 3 3 3
3 1 0
7 8 7 6 8 8 10 6 6 6 4 5 3 5 3 3 4 3 4 3 3 5 2 3 3 2 4 3 3 5 4 1 2 0 1 3 1 0 2
2 0
7 10 9 8 9 9 6 13 8 9 6 8 7 7 5 5 7 6 4 3 2 7 4 4 4 5 5 4 4 6 5 3 1 2 2 1 1 3 2
1 3
8 10 8 6 7 9 6 8 12 9 5 5 3 6 4 5 4 5 3 3 4 8 6 4 4 4 7 3 5 7 5 0 1 3 0 1 1 2 3
3 2
8 9 8 7 10 10 6 9 9 13 7 7 5 5 4 6 4 3 4 4 2 7 5 2 4 3 5 4 6 7 4 1 1 3 2 1 1 3
0 3 1
5 5 5 4 6 7 4 6 5 7 7 5 3 4 3 4 4 2 3 3 1 4 3 0 2 2 3 2 3 5 3 2 0 2 2 2 0 2 0 2
0
5 7 7 6 9 7 5 8 5 7 5 9 6 6 3 4 5 3 4 3 2 6 2 3 3 2 4 4 4 5 3 2 2 0 2 2 2 2 0 2
2
3 6 5 5 7 5 3 7 3 5 3 6 7 4 2 3 4 3 3 2 1 4 1 3 3 2 2 3 3 3 2 2 2 0 2 0 2 2 0 0
2
5 8 6 5 7 7 5 7 6 5 4 6 4 8 4 3 5 3 3 2 3 6 3 3 2 2 5 2 3 4 3 2 0 0 0 2 2 2 2 2
2
4 6 6 4 4 4 3 5 4 4 3 3 2 4 5 3 3 2 1 0 2 3 3 1 1 1 2 1 2 3 2 2 0 0 0 0 0 2 2 2
0
3 6 6 5 5 4 3 5 5 6 4 4 3 3 3 6 2 3 3 1 1 4 3 1 2 1 2 2 4 4 3 2 2 2 0 0 0 2 0 2
0
5 5 5 4 6 7 4 7 4 4 4 5 4 5 3 2 7 3 2 2 1 4 2 2 2 3 3 2 1 4 3 2 0 0 2 2 0 2 2 0
2
3 5 5 4 3 3 3 6 5 3 2 3 3 3 2 3 3 6 3 1 1 4 2 3 3 3 3 2 2 3 3 2 2 2 0 0 0 0 2 0
2
2 4 3 3 4 5 4 4 3 4 3 4 3 3 1 3 2 3 6 3 1 4 1 2 3 1 3 1 3 3 3 2 2 2 0 2 2 0 0 0
0
3 2 1 1 4 6 3 3 3 4 3 3 2 2 0 1 2 1 3 5 1 3 1 1 3 2 3 1 2 3 2 0 0 2 2 2 2 0 0 0
0
3 5 3 2 3 4 3 2 4 2 1 2 1 3 2 1 1 1 1 1 4 3 2 2 2 1 3 1 2 2 1 0 0 0 0 0 2 0 2 2
0
6 8 6 5 7 8 5 7 8 7 4 6 4 6 3 4 4 4 4 3 3 9 4 4 4 3 6 3 5 6 5 0 2 2 0 2 2 2 2 2
2
4 5 4 3 3 5 2 4 6 5 3 2 1 3 3 3 2 2 1 1 2 4 5 1 2 2 3 1 3 4 3 0 0 2 0 0 0 2 2 2
0
3 5 4 3 3 3 3 4 4 2 0 3 3 3 1 1 2 3 2 1 2 4 1 5 3 2 3 2 2 2 2 0 2 0 0 0 2 0 2 0
2
4 5 4 3 4 6 3 4 4 4 2 3 3 2 1 2 2 3 3 3 2 4 2 3 6 3 3 2 3 4 3 0 2 2 2 0 2 0 2 0
0
4 3 3 2 3 4 2 5 4 3 2 2 2 2 1 1 3 3 1 2 1 3 2 2 3 5 3 2 1 3 2 0 0 2 2 0 0 0 2 0
2
5 6 4 2 5 6 4 5 7 5 3 4 2 5 2 2 3 3 3 3 3 6 3 3 3 3 7 2 3 4 3 0 0 2 0 2 2 0 2 2
2
4 3 4 4 5 2 3 4 3 4 2 4 3 2 1 2 2 2 1 1 1 3 1 2 2 2 2 5 2 3 1 0 2 0 2 0 0 0 0 2
2
3 6 4 4 5 5 3 4 5 6 3 4 3 3 2 4 1 2 3 2 2 5 3 2 3 1 3 2 6 4 3 0 2 2 0 0 2 2 0 2
0
7 6 6 5 6 8 5 6 7 7 5 5 3 4 3 4 4 3 3 3 2 6 4 2 4 3 4 3 4 8 5 0 2 2 2 2 0 2 2 2
0
4 5 4 4 3 6 4 5 5 4 3 3 2 3 2 3 3 3 3 2 1 5 3 2 3 2 3 1 3 5 6 0 2 2 0 2 0 2 2 0
0
0 2 3 2 2 1 1 3 0 1 2 2 2 2 2 2 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0
0
1 2 3 3 2 0 2 1 1 1 0 2 2 0 0 2 0 2 2 0 0 2 0 2 2 0 0 2 2 2 2 0 4 0 0 0 0 0 0 0
0
1 1 0 0 0 2 0 2 3 3 2 0 0 0 0 2 0 2 2 2 0 2 2 0 2 2 2 0 2 2 2 0 0 4 0 0 0 0 0 0
0
3 0 1 1 3 3 1 2 0 2 2 2 2 0 0 0 2 0 0 2 0 0 0 0 2 2 0 2 0 2 0 0 0 0 4 0 0 0 0 0
0
1 0 0 0 2 3 3 1 1 1 2 2 0 2 0 0 2 0 2 2 0 2 0 0 0 0 2 0 0 2 2 0 0 0 0 4 0 0 0 0
0
0 3 0 0 2 3 1 1 1 1 0 2 2 2 0 0 0 0 2 2 2 2 0 2 2 0 2 0 2 0 0 0 0 0 0 0 4 0 0 0
0
1 3 2 3 2 3 0 3 2 3 2 2 2 2 2 2 2 0 0 0 0 2 2 0 0 0 0 0 2 2 2 0 0 0 0 0 0 4 0 0
0
3 3 3 1 0 3 2 2 3 0 0 0 0 2 2 0 2 2 0 0 2 2 2 2 2 2 2 0 0 2 2 0 0 0 0 0 0 0 4 0
0
3 3 3 2 3 1 2 1 3 3 2 2 0 2 2 2 0 0 0 0 2 2 2 0 0 0 2 2 2 2 0 0 0 0 0 0 0 0 0 4
0
1 1 1 1 2 0 0 3 2 1 0 2 2 2 0 0 2 2 0 0 0 2 0 2 0 2 2 2 0 0 0 0 0 0 0 0 0 0 0 0
4
-
MINIMUM
4
-
KISSING_NUMBER
15426
-
NOTES
Constructed by Masaaki Harada from an extremal code modulo 4
Basis needs to be divided by 2
-
LAST_LINE
Haftungsausschluss/Disclaimer
Gabriele Nebe