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 13:28:30 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
MINIMAL_NORM
DET
KISSING_NUMBER
GRAM
GROUP_ORDER
GROUP
NOTES
REFERENCES
LAST_LINE

• NAME
  dim13kis672.std
  

• DIMENSION
  13
  

• MINIMAL_NORM
  8
  

• DET
  [ 1, 1, 1, 1, 1, 1, 4, 4, 4, 4, 28, 28, 56 ]
  

• KISSING_NUMBER
  672
  

• GRAM
  13
  [ 8 -4 4 2 1 -2 2 3 3 -2 -2 4 4]
  [-4 8 -4 -4 2 3 2 1 1 4 4 -4 -4]
  [ 4 -4 8 0 2 1 2 -1 -1 0 -4 0 0]
  [ 2 -4 0 8 -4 0 -4 2 0 -4 0 4 4]
  [ 1 2 2 -4 8 3 4 2 -1 0 -2 -2 -3]
  [-2 3 1 0 3 8 2 1 0 0 -1 -2 -4]
  [ 2 2 2 -4 4 2 8 2 0 0 -2 0 -2]
  [ 3 1 -1 2 2 1 2 8 0 -2 -1 2 0]
  [ 3 1 -1 0 -1 0 0 0 8 0 1 0 3]
  [-2 4 0 -4 0 0 0 -2 0 8 4 -4 -4]
  [-2 4 -4 0 -2 -1 -2 -1 1 4 8 0 0]
  [ 4 -4 0 4 -2 -2 0 2 0 -4 0 8 4]
  [ 4 -4 0 4 -3 -4 -2 0 3 -4 0 4 8]
  

• GROUP_ORDER
  [ <2, 11>, <3, 1>, <7, 1> ]
  

• GROUP
  2
  13
  [ 0 0 1 0 0 0 0 0 0 0 0 0 0]
  [ 1 0 -1 0 0 0 0 0 0 0 0 0 0]
  [ 1 0 0 -1 -1 1 0 0 -1 0 0 0 0]
  [ 0 1 1 -1 0 0 -1 0 0 -1 0 0 0]
  [-1 -1 0 0 0 0 1 1 0 1 0 0 1]
  [ 1 0 -1 -1 0 1 0 0 -1 0 0 0 1]
  [ 0 -1 0 0 0 0 1 0 0 0 1 0 0]
  [ 0 1 1 0 0 -1 0 0 0 -1 0 0 0]
  [ 1 0 -1 1 1 0 0 -1 0 1 -1 0 0]
  [ 2 0 -1 -1 -1 1 -1 0 -1 0 0 0 0]
  [ 1 1 0 0 0 0 -1 0 0 0 0 0 0]
  [-2 1 2 1 1 -1 0 0 1 0 0 1 0]
  [-1 0 1 1 1 -1 0 0 1 0 0 0 -1]
  13
  [ 1 -1 0 -2 -1 1 -1 1 -1 -1 1 -1 0]
  [-1 0 0 1 1 -1 1 0 1 0 0 0 0]
  [ 1 0 0 -2 -1 1 -1 0 -1 -1 0 0 0]
  [ 2 1 0 -1 -1 1 -1 0 -1 0 0 0 0]
  [-2 -1 1 -1 0 0 0 1 1 -1 1 0 0]
  [ 0 0 0 -1 0 1 0 0 0 0 0 0 1]
  [ 0 -1 0 -1 0 0 0 0 0 -1 1 -1 0]
  [ 0 0 1 -1 -1 0 0 1 0 -1 1 -1 0]
  [-1 -1 0 0 1 0 0 1 0 1 0 0 1]
  [ 0 -1 -1 0 0 0 1 0 0 0 0 0 0]
  [ 1 0 -1 0 0 0 0 0 0 0 0 0 0]
  [ 2 0 0 -1 -1 1 -1 0 -1 -1 1 -1 0]
  [ 1 1 0 0 0 0 -1 0 -1 0 0 0 0]
  

• NOTES
  Perfect lattice found by Yoav Kallus using an annealing strategy
  

• REFERENCES
  

• LAST_LINE
  

  ---

  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe