The Lattice OBW16

An entry from the Catalogue of Lattices, which is a joint project of
Neil J. A. Sloane, AT&T Labs-Research (njas@research.att.com) and
Gabriele Nebe, University of Ulm (nebe@mathematik.uni-ulm.de)

Last modified Wed Jul 21 15:31:19 EDT 1999

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)
  
  

INDEX FILE | ABBREVIATIONS

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