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 13:18:28 CEST 2014

INDEX FILE | ABBREVIATIONS

Contents of this file

NAME
DIMENSION
DET
MINIMAL_NORM
KISSING_NUMBER
HERMITE_NUMBER
DIVISORS
BASIS
TRIANGULAR_BASIS
GRAM
PROPERTIES
NOTES
REFERENCES
LAST_LINE

• NAME
  LAMBDA13
  

• DIMENSION
  13
  

• DET
  1024
  

• MINIMAL_NORM
  4
  

• KISSING_NUMBER
  906
  

• HERMITE_NUMBER
  .234692093077E+01
  

• DIVISORS
  2^4*4^3
  

• BASIS
  13 24
  .000000000000E+00 .000000000000E+00 .400000000000E+01
  -.400000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .400000000000E+01 -.400000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .400000000000E+01
  .400000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .400000000000E+01 .400000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .400000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .400000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .200000000000E+01 .200000000000E+01 .200000000000E+01
  .200000000000E+01 .200000000000E+01 .200000000000E+01
  .200000000000E+01 .200000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .400000000000E+01 .400000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .400000000000E+01
  .400000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .400000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .400000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .200000000000E+01
  .200000000000E+01 .200000000000E+01 .200000000000E+01
  .200000000000E+01 .200000000000E+01 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .400000000000E+01 .400000000000E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .400000000000E+01 .400000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .200000000000E+01 -.200000000000E+01 .000000000000E+00
  .000000000000E+00 .200000000000E+01 .200000000000E+01
  .000000000000E+00 .000000000000E+00 .200000000000E+01
  -.200000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  

• TRIANGULAR_BASIS
  13 13
  .200000000000E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  -.100000000000E+01 .173205080757E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 -.115470053838E+01 .163299316186E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .115470053838E+01 .816496580928E+00
  .141421356237E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .141421356237E+01 .141421356237E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .122474487139E+01
  .707106781187E+00 .707106781187E+00 .122474487139E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .163299316186E+01
  .115470053838E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .163299316186E+01
  -.577350269190E+00 .100000000000E+01 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .141421356237E+01 -.362597321469E-15
  .512790049702E-15 .888178419700E-15 .141421356237E+01
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .707106781187E+00 .122474487139E+01
  .000000000000E+00 .000000000000E+00 .707106781187E+00
  .122474487139E+01 .000000000000E+00 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .163299316186E+01 .115470053838E+01 .000000000000E+00
  .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .163299316186E+01 -.577350269190E+00 .100000000000E+01
  .000000000000E+00
  .000000000000E+00 -.577350269190E+00 .816496580928E+00
  .000000000000E+00 .000000000000E+00 .000000000000E+00
  .000000000000E+00 .100000000000E+01 -.628036983474E-15
  .816496580928E+00 .577350269190E+00 -.666133814775E-15
  .100000000000E+01
  

• GRAM
  13 13
  4 -2 0 0 0 0 0 0 0 0 0 0 0
  -2 4 -2 2 0 0 0 0 0 0 0 0 -1
  0 -2 4 0 0 2 0 0 0 0 0 0 2
  0 2 0 4 2 2 0 0 0 0 0 0 0
  0 0 0 2 4 2 0 0 2 1 0 0 0
  0 0 2 2 2 4 2 2 1 2 0 0 1
  0 0 0 0 0 2 4 2 0 2 0 0 0
  0 0 0 0 0 2 2 4 0 2 0 0 1
  0 0 0 0 2 1 0 0 4 2 0 0 0
  0 0 0 0 1 2 2 2 2 4 2 2 1
  0 0 0 0 0 0 0 0 0 2 4 2 2
  0 0 0 0 0 0 0 0 0 2 2 4 1
  0 -1 2 0 0 1 0 1 0 1 2 1 4
  

• PROPERTIES
  INTEGRAL =1
  

• NOTES
  A laminated lattice.
  There are three inequivalent 13-dim. laminated lattices; this is Lambda^{max}_13,
  the one with the highest kissing number.
  

• REFERENCES
  1. SPLAG p. 157.
  2. W.Plesken, M.Pohst, Constructing integral lattices with prescribed minimum II,
  Math. Comp. Vol 60, N. 202 (1993) 817-825
  

• LAST_LINE
  

  ---

  Haftungsausschluss/Disclaimer
  
  
  Gabriele Nebe