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 13:27:45 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
BASIS
GRAM
MINIMUM
KISSING_NUMBER
NOTES
LAST_LINE

• NAME
  L36
  

• DIMENSION
  36
  

• DET
  1
  

• BASIS
  36 36
  -1 1 0 0 0 0 0 1 1 0 -1 1 0 0 -1 1 -1 0 -1 0 0 -1 0 0 0 0 1 0 -1 1 1 0 1 0 2 0
  0 -1 0 0 0 0 2 -1 -1 0 0 -1 0 0 0 -1 0 -1 0 0 0 0 -1 -1 -1 0 -1 0 0 -1 0 -1 1
  -1 -1 -1
  -1 0 0 0 0 0 0 2 0 0 -1 0 0 0 -1 0 -1 -1 -1 0 0 -1 -1 -1 -1 0 0 0 -1 0 1 -1 0 1
  -1 -1
  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 2 0 0 0 2
  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 2 0 2 0 2 0
  0 0 0 0 0 0 -2 0 0 0 2 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 -2 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 -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 0 2 0 0 0 0 2
  -1 0 0 1 0 0 -1 1 0 2 0 1 1 0 -1 0 0 0 -1 0 1 0 -1 -1 0 1 1 1 0 1 1 0 0 0 0 0
  0 0 0 0 1 0 0 1 1 1 -1 0 1 0 1 1 0 0 1 1 1 0 0 1 0 1 1 0 0 1 -1 0 -1 1 -1 1
  0 0 0 0 -1 1 1 0 0 0 0 1 0 1 0 0 1 1 0 0 -1 0 0 -1 0 -1 -1 0 0 -1 -1 0 1 1 -1
  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 2 2 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 -2 0 0 -2 0
  0 0 0 0 0 0 0 -2 0 0 0 -2 0 0 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 -2 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 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 2 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 0 0 2 2
  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 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 0 0 0 0 2 2
  0 0 0 0 0 0 0 0 0 0 0 -2 0 0 0 0 0 0 2 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 -2 0 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 -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 2 0
  0 0 0 0 0 0 2 -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 -2
  0 0 0 0 0 1 -1 -1 -1 -1 1 -1 1 1 1 1 -1 1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 -1
  0 0 0 0 0 0 0 2 0 -2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 -2 0 0 0
  -1 1 0 0 0 0 0 1 1 0 -1 -1 0 0 -1 1 1 0 -1 0 0 1 0 0 0 0 1 0 -1 1 -1 0 1 0 0 0
  0 -1 1 0 0 -1 0 2 0 -1 0 0 1 0 -1 -1 0 -1 0 0 0 0 -1 0 0 1 -1 1 1 0 0 -1 1 1 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 -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 2 -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 2 0 0 0 0 0 0 0 0 -2 0 -2
  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 2 0 0 0 0 0 0 0 0 0 0
  0 0 1 -1 0 0 0 1 0 0 0 1 -1 1 0 1 0 0 1 1 1 -1 0 1 0 0 1 0 0 0 0 1 0 1 0 1
  0 -2 0 0 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 0 0 0 -1 1 1 -1 -1 -1 -1 1 -1 1 1 -1 -1 1 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
  -1
  -1 -1 0 0 1 0 0 -2 0 1 0 -1 -1 0 0 0 1 0 0 1 1 1 0 1 0 1 0 0 1 0 0 0 0 -1 -1 1
  0 -1 -1 -1 0 1 1 -1 0 1 1 -1 0 0 1 1 -1 0 0 0 -1 -1 -1 0 -1 0 0 0 0 -1 0 0 1 0
  -1 1
  

• GRAM
  36 36
  5 -2 2 0 2 -1 0 1 2 0 -1 1 -1 -1 -1 2 1 2 1 -2 1 1 -1 -1 0 2 0 -1 1 0 0 1 -1 0
  -2 -1
  -2 5 1 -1 1 -1 1 -1 -1 -2 1 -1 0 2 1 -1 -2 -1 -1 1 0 0 2 0 -1 -1 1 -1 -2 0 1 -2
  1 1 1 2
  2 1 5 -1 0 -1 -1 0 2 0 0 0 1 -1 -1 -1 -2 0 -1 0 -1 0 -1 -1 1 1 2 -1 -1 -1 0 0 0
  1 -2 0
  0 -1 -1 3 -1 0 1 1 1 1 0 1 -1 -1 -1 1 2 0 1 0 1 -1 -1 -1 -1 0 -1 0 1 -1 -1 1 -1
  -1 1 1
  2 1 0 -1 5 -2 0 1 -1 -2 0 1 -2 0 0 2 1 2 1 -1 2 2 1 0 0 0 1 -2 1 0 2 0 1 1 -1
  0
  -1 -1 -1 0 -2 3 -1 -1 0 0 0 0 1 0 0 0 0 -1 0 0 0 0 -1 1 0 0 0 1 -1 0 -1 0 0 -1
  0 0
  0 1 -1 1 0 -1 4 1 1 -1 -1 -1 0 2 1 0 0 1 0 0 0 -1 1 0 -2 -1 -2 -1 1 1 -1 -1 -1
  -1 2 1
  1 -1 0 1 1 -1 1 3 1 0 0 1 0 -1 0 1 1 2 1 -1 1 0 -1 -1 0 -1 0 -1 1 -1 0 1 0 -1 0
  0
  2 -1 2 1 -1 0 1 1 5 1 -1 0 1 -1 -1 0 0 1 0 -1 0 -1 -1 -1 0 1 1 -1 0 0 -1 0 -1
  -1 0 -1
  0 -2 0 1 -2 0 -1 0 1 5 -1 1 1 -1 0 0 0 -1 0 1 -1 -1 -1 0 1 1 0 1 0 -1 0 2 -1 1
  1 0
  -1 1 0 0 0 0 -1 0 -1 -1 4 1 0 -1 0 0 0 0 -1 0 0 -1 1 0 -1 0 0 0 -2 0 0 0 0 -1
  -1 1
  1 -1 0 1 1 0 -1 1 0 1 1 4 0 -1 0 2 1 0 1 0 2 0 -1 -1 -1 1 1 -1 -1 -2 0 1 -1 -1
  0 1
  -1 0 1 -1 -2 1 0 0 1 1 0 0 4 1 1 -1 -2 -1 -1 1 -1 -1 -1 1 0 0 1 0 -2 0 -1 -1 0
  0 0 0
  -1 2 -1 -1 0 0 2 -1 -1 -1 -1 -1 1 4 2 0 -1 -1 0 1 0 0 1 1 -1 0 -1 0 -1 1 0 -2 0
  0 2 1
  -1 1 -1 -1 0 0 1 0 -1 0 0 0 1 2 3 0 -1 0 0 0 0 0 1 1 -1 -1 -1 0 -1 0 0 -1 0 0 1
  1
  2 -1 -1 1 2 0 0 1 0 0 0 2 -1 0 0 4 2 1 2 -1 2 1 -1 0 -1 1 0 -1 0 -1 0 1 0 0 0
  1
  1 -2 -2 2 1 0 0 1 0 0 0 1 -2 -1 -1 2 4 1 2 -1 2 0 -1 0 0 0 -1 0 2 0 0 1 0 -1 0
  0
  2 -1 0 0 2 -1 1 2 1 -1 0 0 -1 -1 0 1 1 4 0 -2 1 1 0 0 0 -1 0 -1 2 0 0 1 0 -1 -1
  -1
  1 -1 -1 1 1 0 0 1 0 0 -1 1 -1 0 0 2 2 0 3 -1 2 1 -1 -1 0 0 0 0 1 -1 0 0 0 0 0
  0
  -2 1 0 0 -1 0 0 -1 -1 1 0 0 1 1 0 -1 -1 -2 -1 3 -1 -1 0 1 0 0 0 0 -1 0 0 0 0 1
  1 1
  1 0 -1 1 2 0 0 1 0 -1 0 2 -1 0 0 2 2 1 2 -1 4 1 -1 -1 -1 0 1 -1 0 -1 0 0 0 -1 0
  0
  1 0 0 -1 2 0 -1 0 -1 -1 -1 0 -1 0 0 1 0 1 1 -1 1 3 0 0 1 0 1 0 1 -1 1 0 1 1 -1
  -1
  -1 2 -1 -1 1 -1 1 -1 -1 -1 1 -1 -1 1 1 -1 -1 0 -1 0 -1 0 4 0 -1 0 -1 0 0 1 1 -1
  0 0 1 0
  -1 0 -1 -1 0 1 0 -1 -1 0 0 -1 1 1 1 0 0 0 -1 1 -1 0 0 4 0 -1 -1 0 0 1 0 0 1 1 0
  1
  0 -1 1 -1 0 0 -2 0 0 1 -1 -1 0 -1 -1 -1 0 0 0 0 -1 1 -1 0 4 0 1 1 1 0 1 1 1 1
  -1 -2
  2 -1 1 0 0 0 -1 -1 1 1 0 1 0 0 -1 1 0 -1 0 0 0 0 0 -1 0 4 0 0 -1 0 0 0 -1 0 0
  -1
  0 1 2 -1 1 0 -2 0 1 0 0 1 1 -1 -1 0 -1 0 0 0 1 1 -1 -1 1 0 5 -1 -1 -1 1 0 1 1
  -1 -1
  -1 -1 -1 0 -2 1 -1 -1 -1 1 0 -1 0 0 0 -1 0 -1 0 0 -1 0 0 0 1 0 -1 3 0 0 0 0 0 0
  0 -1
  1 -2 -1 1 1 -1 1 1 0 0 -2 -1 -2 -1 -1 0 2 2 1 -1 0 1 0 0 1 -1 -1 0 5 0 0 1 0 0
  0 -1
  0 0 -1 -1 0 0 1 -1 0 -1 0 -2 0 1 0 -1 0 0 -1 0 -1 -1 1 1 0 0 -1 0 0 4 0 -1 0 0
  0 -1
  0 1 0 -1 2 -1 -1 0 -1 0 0 0 -1 0 0 0 0 0 0 0 0 1 1 0 1 0 1 0 0 0 3 0 1 1 0 0
  1 -2 0 1 0 0 -1 1 0 2 0 1 -1 -2 -1 1 1 1 0 0 0 0 -1 0 1 0 0 0 1 -1 0 4 0 0 0 0
  -1 1 0 -1 1 0 -1 0 -1 -1 0 -1 0 0 0 0 0 0 0 0 0 1 0 1 1 -1 1 0 0 0 1 0 3 1 0 0
  0 1 1 -1 1 -1 -1 -1 -1 1 -1 -1 0 0 0 0 -1 -1 0 1 -1 1 0 1 1 0 1 0 0 0 1 0 1 4
  -1 0
  -2 1 -2 1 -1 0 2 0 0 1 -1 0 0 2 1 0 0 -1 0 1 0 -1 1 0 -1 0 -1 0 0 0 0 0 0 -1 5
  1
  -1 2 0 1 0 0 1 0 -1 0 1 1 0 1 1 1 0 -1 0 1 0 -1 0 1 -2 -1 -1 -1 -1 -1 0 0 0 0 1
  5
  

• MINIMUM
  3
  

• KISSING_NUMBER
  960
  

• NOTES
  Constructed by Masaaki Harada from an extremal code modulo 4
  Unimodular lattice with long shadow as investigated by Venkov/Nebe
  

• LAST_LINE
  

  ---

  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe