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 13:11:03 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME (required)
DIMENSION (required)
GRAM (floating point or integer Gram matrix)
DIVISORS (elementary divisors)
MINIMAL_NORM
PROPERTIES
REFERENCES
LAST_LINE (required)

• NAME (required)
  Bhurw8
  

• DIMENSION (required)
  32
  

• GRAM (floating point or integer Gram matrix)
  32
  8 4 -4 -4 4 4 -4 -4 4 2 2 -2 0 -2 4 -2 2 -4 2 4 -2 2 4 2 0 3 -1 -1 4 -3 -4 -3
  4 8 -4 -4 4 4 0 -4 2 2 4 -2 2 0 0 0 -2 -4 2 2 -2 0 2 0 -1 1 -2 1 3 -4 -4 -2
  -4 -4 8 0 0 -4 0 4 -2 0 -2 0 2 2 0 2 -2 4 -2 -4 2 0 0 0 -1 0 3 -2 -1 3 2 3
  -4 -4 0 8 -4 0 0 0 -2 -4 -2 4 -2 2 -4 -2 0 2 -2 0 0 0 -2 -2 3 -2 -1 2 -3 3 4 1
  4 4 0 -4 8 4 -4 0 4 4 0 -4 4 2 2 2 -2 -2 2 2 0 0 4 2 -2 4 0 -2 2 -3 -5 -1
  4 4 -4 0 4 8 -4 -4 4 0 0 0 2 2 0 0 0 -2 0 4 -2 2 4 0 2 2 -2 0 1 -3 -4 -2
  -4 0 0 0 -4 -4 8 0 -2 0 2 0 0 -2 -2 0 -2 2 0 -2 0 -2 -4 0 -1 -4 -1 2 -2 1 3 0
  -4 -4 4 0 0 -4 0 8 -2 2 -4 -2 0 2 0 4 0 2 0 -4 2 -2 -2 0 -1 1 2 -1 -2 1 0 2
  4 2 -2 -2 4 4 -2 -2 8 4 -2 0 4 2 4 2 0 0 0 2 -2 3 5 3 2 3 -1 1 2 -1 -3 -3
  2 2 0 -4 4 0 0 2 4 8 -2 -4 4 2 4 4 -2 0 2 0 -1 0 3 4 -1 4 -1 0 2 -1 -3 -3
  2 4 -2 -2 0 0 2 -4 -2 -2 8 -2 0 -4 -2 -4 0 -2 2 2 -1 -1 -2 -1 -2 -2 0 0 2 -2 1 1
  -2 -2 0 4 -4 0 0 -2 0 -4 -2 8 -2 2 -2 -2 2 0 -2 0 -1 2 1 -2 3 -2 1 2 -1 3 2 0
  0 2 2 -2 4 2 0 0 4 4 0 -2 8 4 0 2 -2 1 1 1 -2 2 3 1 0 2 1 -1 2 0 -1 -1
  -2 0 2 2 2 2 -2 2 2 2 -4 2 4 8 -2 2 -1 0 -1 -1 -2 2 3 0 2 2 1 0 0 2 -1 -1
  4 0 0 -4 2 0 -2 0 4 4 -2 -2 0 -2 8 2 1 1 0 0 1 2 3 3 0 3 -1 0 2 -1 -2 -2
  -2 0 2 -2 2 0 0 4 2 4 -4 -2 2 2 2 8 -3 3 -2 -4 2 -1 1 2 0 2 0 1 -1 -1 -3 0
  2 -2 -2 0 -2 0 -2 0 0 -2 0 2 -2 -1 1 -3 8 -1 0 1 0 3 -1 -2 2 1 1 -2 2 1 1 0
  -4 -4 4 2 -2 -2 2 2 0 0 -2 0 1 0 1 3 -1 8 -4 -4 3 1 -1 0 2 0 0 0 -2 3 3 2
  2 2 -2 -2 2 0 0 0 0 2 2 -2 1 -1 0 -2 0 -4 6 3 -1 -2 0 1 -2 0 0 0 1 -2 -2 -1
  4 2 -4 0 2 4 -2 -4 2 0 2 0 1 -1 0 -4 1 -4 3 8 -3 1 2 0 -1 1 -1 -1 1 -2 -1 -3
  -2 -2 2 0 0 -2 0 2 -2 -1 -1 -1 -2 -2 1 2 0 3 -1 -3 6 -1 -3 0 -1 0 0 -1 -1 1 1 3
  2 0 0 0 0 2 -2 -2 3 0 -1 2 2 2 2 -1 3 1 -2 1 -1 6 2 -1 3 2 0 -1 3 2 1 -1
  4 2 0 -2 4 4 -4 -2 5 3 -2 1 3 3 3 1 -1 -1 0 2 -3 2 8 2 1 3 1 0 2 -1 -4 -3
  2 0 0 -2 2 0 0 0 3 4 -1 -2 1 0 3 2 -2 0 1 0 0 -1 2 6 -1 1 0 1 0 0 -2 -2
  0 -1 -1 3 -2 2 -1 -1 2 -1 -2 3 0 2 0 0 2 2 -2 -1 -1 3 1 -1 6 1 -2 2 1 2 1 0
  3 1 0 -2 4 2 -4 1 3 4 -2 -2 2 2 3 2 1 0 0 1 0 2 3 1 1 6 -1 -2 3 0 -2 -1
  -1 -2 3 -1 0 -2 -1 2 -1 -1 0 1 1 1 -1 0 1 0 0 -1 0 0 1 0 -2 -1 6 -2 0 1 0 1
  -1 1 -2 2 -2 0 2 -1 1 0 0 2 -1 0 0 1 -2 0 0 -1 -1 -1 0 1 2 -2 -2 6 -1 0 0 -1
  4 3 -1 -3 2 1 -2 -2 2 2 2 -1 2 0 2 -1 2 -2 1 1 -1 3 2 0 1 3 0 -1 6 0 -1 -1
  -3 -4 3 3 -3 -3 1 1 -1 -1 -2 3 0 2 -1 -1 1 3 -2 -2 1 2 -1 0 2 0 1 0 0 6 4 1
  -4 -4 2 4 -5 -4 3 0 -3 -3 1 2 -1 -1 -2 -3 1 3 -2 -1 1 1 -4 -2 1 -2 0 0 -1 4 8 3
  -3 -2 3 1 -1 -2 0 2 -3 -3 1 0 -1 -1 -2 0 0 2 -1 -3 3 -1 -3 -2 0 -1 1 -1 -1 1 3 6
  

• DIVISORS (elementary divisors)
  1^16*2^16
  

• MINIMAL_NORM
  6
  

• PROPERTIES
  INTEGRAL = 1
  MODULAR = 2
  

• REFERENCES
  C. Bachoc,
  "Voisinage au sens de Kneser pour les reseaux quaternioniens",
  Comm. Math. Helvetici (1995) 350-374.
  

• LAST_LINE (required)
  
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe