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 So 1. Sep 15:25:33 CEST 2024

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
MINIMAL_NORM
KISSING_NUMBER
GRAM
PROPERTIES
NOTES
LAST_LINE

• NAME
  U28
  

• DIMENSION
  28
  

• DET
  1
  

• MINIMAL_NORM
  3
  

• KISSING_NUMBER
  2240
  

• GRAM
  28 28
  3 1 -1 0 0 0 -1 0 0 -1 0 0 0 0 1 0 -1 1 1 0 1 0 -1 1 -1 0 0 1
  1 3 0 0 0 0 0 1 0 0 1 0 1 0 0 0 -1 1 0 -1 1 0 0 1 -1 0 0 0
  -1 0 3 -1 0 -1 0 0 0 0 0 0 0 0 -1 0 1 -1 -2 -1 0 0 0 -1 0 -1 1 -1
  0 0 -1 3 0 0 0 0 0 0 0 -1 1 0 0 -1 -1 1 2 1 1 -1 -1 0 0 1 -1 1
  0 0 0 0 3 2 1 1 0 1 1 0 0 1 0 1 1 0 0 -1 -1 0 1 -1 0 1 0 1
  0 0 -1 0 2 4 2 1 -1 2 2 1 0 2 1 2 1 0 0 0 -1 1 1 0 1 2 0 2
  -1 0 0 0 1 2 4 1 -2 2 2 0 0 2 0 1 2 1 0 -1 -1 2 1 0 2 1 1 2
  0 1 0 0 1 1 1 4 -1 2 0 0 0 0 1 0 1 1 0 0 2 1 0 1 -1 1 0 2
  0 0 0 0 0 -1 -2 -1 4 -1 0 -1 0 -2 -2 -1 -2 0 0 0 -1 -2 -1 0 -1 -1 -2 -2
  -1 0 0 0 1 2 2 2 -1 4 1 0 0 1 0 1 2 0 -1 -1 0 2 1 0 1 1 0 2
  0 1 0 0 1 2 2 0 0 1 4 0 0 1 -1 1 0 2 -1 -2 -1 1 0 0 1 1 -1 1
  0 0 0 -1 0 1 0 0 -1 0 0 4 1 1 0 0 0 -1 -1 1 0 1 1 1 0 0 0 -1
  0 1 0 1 0 0 0 0 0 0 0 1 4 1 0 0 -1 0 1 1 1 -1 -1 1 0 0 0 -1
  0 0 0 0 1 2 2 0 -2 1 1 1 1 4 2 2 2 -1 0 0 -1 1 1 -1 2 2 2 2
  1 0 -1 0 0 1 0 1 -2 0 -1 0 0 2 4 2 1 -1 1 1 1 0 0 0 0 2 2 2
  0 0 0 -1 1 2 1 0 -1 1 1 0 0 2 2 4 1 -1 -1 -1 -1 0 0 0 0 2 2 1
  -1 -1 1 -1 1 1 2 1 -2 2 0 0 -1 2 1 1 4 -1 -1 -1 -1 2 2 -2 2 0 2 2
  1 1 -1 1 0 0 1 1 0 0 2 -1 0 -1 -1 -1 -1 4 1 -1 1 1 -1 1 0 0 -2 1
  1 0 -2 2 0 0 0 0 0 -1 -1 -1 1 0 1 -1 -1 1 4 2 1 -1 -1 1 0 0 0 1
  0 -1 -1 1 -1 0 -1 0 0 -1 -2 1 1 0 1 -1 -1 -1 2 4 1 -1 -1 1 0 0 0 0
  1 1 0 1 -1 -1 -1 2 -1 0 -1 0 1 -1 1 -1 -1 1 1 1 4 0 -2 2 -2 0 0 1
  0 0 0 -1 0 1 2 1 -2 2 1 1 -1 1 0 0 2 1 -1 -1 0 4 2 0 2 0 0 2
  -1 0 0 -1 1 1 1 0 -1 1 0 1 -1 1 0 0 2 -1 -1 -1 -2 2 4 -2 2 0 0 0
  1 1 -1 0 -1 0 0 1 0 0 0 1 1 -1 0 0 -2 1 1 1 2 0 -2 4 -2 0 0 0
  -1 -1 0 0 0 1 2 -1 -1 1 1 0 0 2 0 0 2 0 0 0 -2 2 2 -2 4 0 0 1
  0 0 -1 1 1 2 1 1 -1 1 1 0 0 2 2 2 0 0 0 0 0 0 0 0 0 4 0 2
  0 0 1 -1 0 0 1 0 -2 0 -1 0 0 2 2 2 2 -2 0 0 0 0 0 0 0 0 4 1
  1 0 -1 1 1 2 2 2 -2 2 1 -1 -1 2 2 1 2 1 1 0 1 2 0 0 1 2 1 5
  

• PROPERTIES
  INTEGRAL =1
  UNIMODULAR =1
  

• NOTES
  odd unimodular lattices of norm 3 constructed from self-dual Z4-code
  by M. Shi, J.L. Kim and S. Tao.
  

• LAST_LINE
  

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  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe