The Lattice 6QF.6.d

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

Last modified Thu Jun 28 23:55:28 EDT 2001

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
MINIMAL_NORM
DET
KISSING_NUMBER
GRAM
GROUP_ORDER
THETA_SERIES
PROPERTIES
NOTES
REFERENCES
LAST_LINE

• NAME
  6QF.6.d
  
• DIMENSION
  6
  
• MINIMAL_NORM
  4
  
• DET
  512
  
• KISSING_NUMBER
  30
  
• GRAM
  6 6
  4 1 -1 -1 1 -1
  1 4 0 1 2 1
  -1 0 4 -1 2 -1
  -1 1 -1 4 -1 0
  1 2 2 -1 4 -1
  -1 1 -1 0 -1 4
  
• GROUP_ORDER
  384
  
• THETA_SERIES
  1+30*q^4+56*q^6+66*q^8+144*q^10+188*q^12+584*q^14+378*q^16+448*q^18
  
• PROPERTIES
  INTEGRAL=1
  MODULAR=8
  
• NOTES
  Fixed sublattice of type 1^2 2 4 8^2 in Leech.
  Strongly 8-modular.
  
• REFERENCES
  E. M. Rains and N. J. A. Sloane,
  The Shadow Theory of Modular and Unimodular Lattices,
  J. Number Theory, 73 (1998), pp. 359-389;
  http://www.research.att.com/~njas/doc/shad.pdf or shad.ps
  
• LAST_LINE
  

INDEX FILE | ABBREVIATIONS

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