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 13:28:43 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
  dim15kis1872.std
  

• DIMENSION
  15
  

• MINIMAL_NORM
  4
  

• DET
  [ 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 4, 4, 12 ]
  

• KISSING_NUMBER
  1872
  

• GRAM
  15
  [ 4 -2 2 -2 -2 2 2 1 -2 -2 -2 1 2 2 -2]
  [-2 4 0 2 2 -2 0 1 1 0 1 -2 -1 0 1]
  [ 2 0 4 -2 0 2 2 2 -2 -1 -2 -1 1 2 -2]
  [-2 2 -2 4 0 -2 0 0 2 1 2 -1 0 0 1]
  [-2 2 0 0 4 -2 0 1 0 0 1 -1 -1 -2 1]
  [ 2 -2 2 -2 -2 4 0 0 -1 -1 -1 0 1 2 -2]
  [ 2 0 2 0 0 0 4 2 -2 -1 -1 -1 2 2 -1]
  [ 1 1 2 0 1 0 2 4 -2 -2 0 -2 2 1 0]
  [-2 1 -2 2 0 -1 -2 -2 4 2 2 1 -1 -1 1]
  [-2 0 -1 1 0 -1 -1 -2 2 4 0 1 -2 -1 0]
  [-2 1 -2 2 1 -1 -1 0 2 0 4 0 0 -1 2]
  [ 1 -2 -1 -1 -1 0 -1 -2 1 1 0 4 -1 -1 0]
  [ 2 -1 1 0 -1 1 2 2 -1 -2 0 -1 4 1 0]
  [ 2 0 2 0 -2 2 2 1 -1 -1 -1 -1 1 4 -2]
  [-2 1 -2 1 1 -2 -1 0 1 0 2 0 0 -2 4]
  

• GROUP_ORDER
  [ <2, 13>, <3, 2> ]
  

• GROUP
  4
  15
  [ 0 0 0 1 0 1 1 0 0 -1 0 0 -1 -1 0]
  [-1 0 -1 -2 -1 0 1 1 1 0 0 0 0 0 0]
  [ 0 -1 0 0 -1 0 1 1 1 -1 0 -1 -2 -1 0]
  [-2 1 -1 -2 -1 0 1 0 0 0 0 1 1 0 -1]
  [ 2 0 0 0 0 0 -1 0 0 1 0 -1 0 0 1]
  [ 0 -1 1 1 0 -1 0 0 0 -1 0 0 -1 0 0]
  [-1 1 -1 -1 -2 1 2 1 1 -1 0 0 -1 -2 -1]
  [ 0 1 -1 -1 -1 1 1 1 0 0 0 0 -1 -1 0]
  [-1 0 0 -1 0 -1 0 -1 0 0 0 0 1 1 0]
  [-2 0 0 -1 -1 -1 0 0 0 0 0 0 1 0 -1]
  [ 1 1 0 -1 0 -1 -1 -1 -1 1 1 0 1 1 0]
  [ 0 0 0 1 1 0 -1 -1 -1 0 0 0 1 1 0]
  [ 1 1 -1 0 0 1 1 0 0 0 0 0 -1 -1 0]
  [-3 0 0 -1 -2 0 2 1 1 -2 0 1 -1 -1 -1]
  [ 1 1 -1 -1 1 0 -1 0 0 1 0 0 1 1 0]
  15
  [ 2 0 -1 0 1 0 -1 0 0 1 0 -1 0 1 1]
  [ 1 0 1 1 1 0 -1 -1 -1 0 0 0 0 0 0]
  [ 0 1 -1 -1 0 0 0 0 0 0 0 0 0 1 0]
  [ 0 0 1 1 0 0 0 -1 -1 0 0 0 0 -1 0]
  [ 0 -1 1 1 0 0 0 0 0 -1 0 0 -1 0 0]
  [-1 1 -1 -1 0 0 0 0 0 0 0 1 1 1 0]
  [ 1 0 0 0 0 0 0 0 0 0 0 -1 -1 0 1]
  [ 0 1 -1 0 0 1 0 0 -1 0 0 0 0 0 0]
  [ 1 0 1 1 0 0 0 -1 0 0 0 0 0 -1 0]
  [-2 0 1 -1 -2 -1 1 0 1 -1 0 0 0 -1 -1]
  [ 1 0 1 1 0 0 0 -1 -1 0 1 0 0 -1 0]
  [ 1 -1 0 0 0 -1 0 0 1 0 0 -1 0 0 0]
  [ 1 1 -1 0 0 1 0 0 -1 1 0 0 0 0 1]
  [ 0 1 -1 -1 0 0 0 0 0 0 0 0 0 0 0]
  [ 0 0 0 0 0 1 1 0 0 0 0 0 0 -1 0]
  15
  [-1 0 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 0 -1 0 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 0 -1 0 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 0 -1 0 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 0 -1 0 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 0 -1 0 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 0 -1 0 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 0 -1]
  15
  [ 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0]
  [ 0 1 0 0 0 1 0 0 0 0 0 0 0 -1 0]
  [ 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0]
  [ 0 0 0 1 0 1 0 0 0 0 0 0 0 -1 0]
  [ 0 1 -1 -1 0 1 0 0 0 0 0 0 0 0 0]
  [ 0 0 1 0 -1 -1 0 0 0 0 0 0 0 0 0]
  [ 0 0 0 0 0 1 1 0 0 0 0 0 0 -1 0]
  [-1 1 0 0 0 1 0 0 -1 0 0 1 1 0 0]
  [ 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0]
  [ 0 -1 0 0 0 0 0 1 1 0 0 0 -1 0 0]
  [-1 1 -1 0 0 1 0 0 0 0 -1 1 1 0 0]
  [ 1 0 -1 0 1 0 0 0 0 1 0 0 0 1 0]
  [ 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0]
  [-1 0 1 0 -1 0 1 0 0 0 0 0 0 -1 0]
  [ 2 0 0 1 2 0 -2 -1 -1 1 0 0 1 1 1]
  

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

• REFERENCES
  

• LAST_LINE
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe