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 13:21:18 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME (required)
DIMENSION (required)
DET
GRAM
DIVISORS (elementary divisors)
MINIMAL_NORM
KISSING_NUMBER
GROUP_ORDER
GROUP_NAME
GROUP_GENERATORS
NOTES
LAST_LINE (required)

• NAME (required)
  OBW16
  

• DIMENSION (required)
  16
  

• DET
  64
  

• GRAM
  16 0
  3
  -1 3
  -1 -1 3
  1 -1 1 3
  0 1 0 -1 3
  -1 0 0 -1 -1 3
  1 0 0 1 -1 -1 3
  -1 0 1 0 1 -1 -1 3
  1 0 -1 0 -1 1 1 -1 3
  -1 0 1 0 -1 0 0 1 -1 3
  0 1 0 1 0 0 1 -1 0 0 3
  1 -1 1 1 -1 0 1 -1 0 0 0 3
  -1 0 1 1 0 -1 0 1 -1 1 0 0 3
  0 0 1 0 1 0 -1 1 -1 0 0 0 -1 3
  1 1 -1 0 0 0 0 -1 0 0 1 0 -1 1 3
  1 -1 -1 1 -1 -1 1 0 0 0 0 0 0 -1 0 3
  

• DIVISORS (elementary divisors)
  2^6
  

• MINIMAL_NORM
  3
  

• KISSING_NUMBER
  512
  

• GROUP_ORDER
  2^18 * 3^4 * 5 * 7
  

• GROUP_NAME
  D8D8D8D8.S6(2)
  

• GROUP_GENERATORS
  3
  16 16
  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 1 0 0
  1 0 0 -1 -1 0 0 1 -1 -1 1 0 0 -1 0 -1
  0 0 0 0 0 0 0 0 -1 0 0 0 -1 -1 0 0
  3 1 2 -2 -3 0 -1 1 -1 -2 1 -1 1 0 0 0
  0 0 0 0 1 0 0 0 1 1 0 0 0 0 0 0
  0 1 0 0 0 0 0 -1 0 0 0 0 0 1 -1 1
  0 0 0 0 -1 0 0 1 -1 -1 0 0 0 -1 1 -1
  0 1 0 0 0 -1 -1 -1 1 1 0 0 0 1 -1 1
  -2 -1 -1 1 1 0 1 1 0 0 0 1 -1 -1 1 -1
  0 0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0
  -1 -1 -2 1 2 1 1 0 0 1 0 1 0 0 0 0
  0 0 0 1 0 0 0 0 -1 0 0 0 -1 -1 0 -1
  0 -1 -1 0 0 1 1 2 -1 -1 0 0 0 -1 1 -1
  -3 -2 -2 2 3 0 1 0 1 1 -1 1 -1 0 1 0
  0 1 1 0 0 0 0 -1 0 0 -1 0 0 0 0 1
  16 16
  -4 -3 -3 3 4 0 1 -1 1 2 -1 1 -1 0 1 -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 0 0 0 0 0 0 0
  0 0 0 0 1 0 0 -1 0 1 0 0 0 0 0 0
  -2 -1 -2 2 2 0 1 -1 1 1 -1 0 0 1 0 0
  1 0 0 -1 -2 0 0 2 -1 -1 1 0 0 -1 0 -1
  -2 -1 -1 2 3 1 1 0 0 1 -1 1 -1 -1 1 0
  2 2 2 -2 -2 -1 -1 -1 0 -1 0 -1 1 1 -1 1
  -3 -2 -2 2 2 0 1 0 0 1 -1 1 -1 -1 1 -1
  2 2 2 -2 -2 -1 -2 0 0 -1 1 0 0 0 -1 1
  0 0 0 1 1 0 0 0 0 1 0 0 -1 -1 0 0
  -2 -1 -1 1 2 0 0 0 1 1 0 1 0 0 1 0
  2 2 1 -1 -1 0 -1 -1 0 0 0 0 1 1 -1 1
  0 0 0 0 0 0 0 0 0 0 0 -1 0 0 0 0
  -1 -1 -1 1 1 0 0 0 0 1 0 0 -1 0 0 0
  1 0 1 -1 0 0 0 0 0 0 0 0 0 0 0 0
  16 16
  1 0 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 0 1 0 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 0 1 0 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 0 1 0 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 0 1 0 0 0 0 0 0 0
  0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0
  -1 0 -1 2 2 1 1 -1 0 1 -1 0 0 0 0 0
  2 1 2 -1 -2 0 0 0 -1 -1 0 -1 0 0 0 0
  -2 -1 -1 1 1 -1 0 -1 1 1 0 0 0 1 0 0
  2 1 1 -1 -1 1 0 1 -1 -1 0 0 1 0 0 0
  2 2 1 -1 -1 0 -1 -1 0 0 0 0 1 1 -1 1
  0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
  

• NOTES
  Overlattice of the Barnes Wall lattice BW16 found by J. Martinet.
  Its minimal vectors form a 5-design.
  

• LAST_LINE (required)
  
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe