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 13:28:32 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
  dim14kis486.std
  

• DIMENSION
  14
  

• MINIMAL_NORM
  36
  

• DET
  [ 1, 1, 1, 1, 3, 3, 3, 3, 18, 18, 54, 54, 13824, 41472 ]
  

• KISSING_NUMBER
  486
  

• GRAM
  14
  [ 36 17 14 14 -9 -9 9 18 -4 18 -14 0 17 -16]
  [ 17 36 -4 19 -18 9 -9 8 12 18 4 9 18 -18]
  [ 14 -4 40 12 -12 3 18 -7 5 -6 2 -18 5 -7]
  [ 14 19 12 38 -8 8 0 -3 19 8 -2 9 1 -3]
  [ -9 -18 -12 -8 36 -18 -9 10 -16 -9 -2 9 -9 9]
  [ -9 9 3 8 -18 36 -9 -19 16 -9 2 -9 0 9]
  [ 9 -9 18 0 -9 -9 36 -9 0 9 0 0 -9 -9]
  [ 18 8 -7 -3 10 -19 -9 38 -17 8 -12 0 8 -8]
  [ -4 12 5 19 -16 16 0 -17 36 7 12 9 -6 1]
  [ 18 18 -6 8 -9 -9 9 8 7 36 2 18 9 -9]
  [-14 4 2 -2 -2 2 0 -12 12 2 36 0 4 -6]
  [ 0 9 -18 9 9 -9 0 0 9 18 0 36 -9 0]
  [ 17 18 5 1 -9 0 -9 8 -6 9 4 -9 36 -18]
  [-16 -18 -7 -3 9 9 -9 -8 1 -9 -6 0 -18 36]
  

• GROUP_ORDER
  [ <2, 4>, <3, 2> ]
  

• GROUP
  5
  14
  [ 0 1 0 0 0 -1 0 -1 0 0 0 -1 -1 0]
  [ 0 0 0 0 0 0 0 0 0 0 0 0 -1 0]
  [ 1 0 -1 0 -1 -1 0 -1 0 -1 0 0 0 0]
  [ 0 2 0 -1 1 -1 0 -1 1 0 -1 -1 -1 0]
  [ 0 1 0 0 1 0 0 0 0 0 0 -1 0 0]
  [ 0 -1 0 0 -1 0 -1 0 0 0 0 1 0 0]
  [ 0 0 0 0 -1 -1 0 0 0 0 0 0 0 0]
  [-1 1 0 0 1 0 1 0 0 0 0 -1 0 0]
  [ 1 -1 -1 0 0 0 0 0 1 0 0 0 0 0]
  [ 0 0 0 0 0 0 0 0 0 1 0 -1 -1 0]
  [ 2 -2 -1 0 -1 1 0 1 0 -1 1 1 0 0]
  [ 0 1 0 0 1 0 0 0 0 1 0 -1 -1 0]
  [ 0 1 0 0 0 0 1 0 0 -1 0 0 0 1]
  [ 0 -1 0 0 0 1 -1 0 0 1 0 0 0 -1]
  14
  [-1 0 0 0 0 0 0 0 0 0 0 0 0 0]
  [ 0 -1 0 0 0 0 0 0 0 0 0 0 0 0]
  [ 0 0 -1 0 0 0 0 0 0 0 0 0 0 0]
  [ 0 0 0 -1 0 0 0 0 0 0 0 0 0 0]
  [ 0 0 0 0 -1 0 0 0 0 0 0 0 0 0]
  [ 0 0 0 0 0 -1 0 0 0 0 0 0 0 0]
  [ 0 0 0 0 0 0 -1 0 0 0 0 0 0 0]
  [ 0 0 0 0 0 0 0 -1 0 0 0 0 0 0]
  [ 0 0 0 0 0 0 0 0 -1 0 0 0 0 0]
  [ 0 0 0 0 0 0 0 0 0 -1 0 0 0 0]
  [ 0 0 0 0 0 0 0 0 0 0 -1 0 0 0]
  [ 0 0 0 0 0 0 0 0 0 0 0 -1 0 0]
  [ 0 0 0 0 0 0 0 0 0 0 0 0 -1 0]
  [ 0 0 0 0 0 0 0 0 0 0 0 0 0 -1]
  14
  [ 1 -2 0 0 0 1 -1 0 0 0 0 1 0 -1]
  [ 0 0 0 0 0 0 0 0 0 -1 0 1 1 0]
  [ 0 -1 0 0 1 1 1 1 1 0 0 0 1 0]
  [ 1 -2 0 0 -1 1 0 1 0 -1 1 2 1 0]
  [ 0 -1 0 0 -1 0 -1 0 0 1 0 0 -1 -1]
  [ 0 1 0 0 0 -1 1 0 0 -1 0 0 1 1]
  [ 0 0 0 0 1 1 1 0 0 0 0 0 0 0]
  [ 1 -1 0 0 0 0 -2 -1 0 1 0 0 -1 -1]
  [-1 1 1 0 0 0 1 1 0 -1 0 1 1 1]
  [ 0 0 0 0 0 0 0 0 0 -1 0 1 0 0]
  [-2 0 0 1 0 0 1 1 0 0 0 0 1 0]
  [ 0 0 0 0 -1 0 0 0 0 -1 0 1 0 0]
  [ 0 -1 0 0 0 0 -1 0 0 0 0 0 0 -1]
  [ 0 0 0 0 -1 -1 0 0 0 0 0 0 0 1]
  14
  [ 0 0 0 0 0 -1 -1 -1 0 0 0 0 0 0]
  [ 0 0 0 0 -1 -1 0 0 0 -1 0 1 1 1]
  [ 1 0 -1 0 1 0 0 -1 0 0 0 -1 0 0]
  [ 0 2 0 -1 1 -1 1 -1 1 -1 -1 0 1 1]
  [ 0 0 0 0 0 0 0 0 0 0 0 0 -1 -1]
  [ 0 0 0 0 0 0 1 0 0 0 0 0 1 1]
  [ 0 0 0 0 1 1 0 0 0 0 0 0 0 0]
  [-1 1 0 0 0 -1 0 0 0 0 0 0 0 0]
  [ 1 0 -1 0 0 0 1 0 1 -1 0 0 1 1]
  [ 0 -1 0 0 -1 0 -1 0 0 0 0 1 0 0]
  [ 2 -2 -1 0 -1 1 0 1 0 -1 1 1 0 0]
  [ 0 0 0 0 -1 0 0 0 0 -1 0 1 0 0]
  [ 0 -1 0 0 -1 -1 -1 0 0 0 0 0 0 0]
  [ 0 -1 0 0 0 1 0 0 0 1 0 0 0 -1]
  14
  [ 1 0 0 0 1 1 0 0 0 0 0 0 0 0]
  [ 0 0 0 0 1 1 1 0 0 0 0 0 1 0]
  [ 0 0 1 0 0 0 -1 0 0 0 0 1 0 0]
  [ 0 -1 0 1 0 0 0 0 0 0 0 0 1 0]
  [ 0 1 0 0 0 -1 0 0 0 0 0 -1 -1 0]
  [ 0 -1 0 0 -1 0 0 0 0 0 0 1 1 0]
  [ 0 0 0 0 0 0 -1 0 0 0 0 0 0 0]
  [ 0 0 0 0 1 1 1 1 0 0 0 0 0 0]
  [ 0 -1 0 0 0 0 0 0 1 0 0 0 1 0]
  [ 0 0 0 0 1 1 0 0 0 1 0 -1 0 0]
  [ 0 0 0 0 0 0 0 0 0 0 1 0 0 0]
  [ 0 0 0 0 0 0 0 0 0 0 0 -1 0 0]
  [ 0 1 0 0 1 1 1 0 0 0 0 0 0 0]
  [ 0 0 0 0 -1 -1 0 0 0 0 0 0 0 1]
  

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

• REFERENCES
  

• LAST_LINE
  

  ---

  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe