The Lattice LAMBDA20
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 13:18:59 CEST 2014
INDEX FILE |
ABBREVIATIONS
Contents of this file
NAME
DIMENSION
DET
MINIMAL_NORM
KISSING_NUMBER
DIVISORS
HERMITE_NUMBER
BASIS
TRIANGULAR_BASIS
GRAM
PROPERTIES
NOTES
REFERENCES
LAST_LINE
-
NAME
LAMBDA20
-
DIMENSION
20
-
DET
64
-
MINIMAL_NORM
4
-
KISSING_NUMBER
17400
-
DIVISORS
2^4*4^2
-
HERMITE_NUMBER
.324900958600E+01
-
BASIS
20 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
.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 .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 .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 .000000000000E+00 .000000000000E+00
.200000000000E+01 .000000000000E+00 .200000000000E+01
.000000000000E+00 .200000000000E+01 .000000000000E+00
.000000000000E+00 .200000000000E+01 .000000000000E+00
.000000000000E+00 .200000000000E+01 -.200000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+01 -.200000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .200000000000E+01 .000000000000E+00
.200000000000E+01 .000000000000E+00 .000000000000E+00
.200000000000E+01 -.200000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .200000000000E+01
-.200000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .200000000000E+01 .000000000000E+00
.200000000000E+01 .000000000000E+00 .000000000000E+00
.200000000000E+01 .200000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .200000000000E+01
.200000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.200000000000E+01 .000000000000E+00 .200000000000E+01
.000000000000E+00 .200000000000E+01 .000000000000E+00
.000000000000E+00 .200000000000E+01 .200000000000E+01
.200000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .200000000000E+01 .200000000000E+01
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
-
TRIANGULAR_BASIS
20 20
.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
-.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 .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 .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 .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
.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
.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
.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 .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 .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 .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 .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 -.577350269190E+00 .816496580928E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .100000000000E+01 -.628036983474E-15
.816496580928E+00 .577350269190E+00 -.666133814775E-15
.100000000000E+01 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.500000000000E+00 .288675134595E+00 .816496580928E+00
-.314018491737E-15 .314018491737E-15 -.362597321469E-15
-.866025403784E+00 -.500000000000E+00 .314018491737E-15
.816496580928E+00 -.288675134595E+00 .500000000000E+00
-.500000000000E+00 .866025403784E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.500000000000E+00 .288675134595E+00 .816496580928E+00
-.314018491737E-15 .314018491737E-15 .816496580928E+00
-.288675134595E+00 .500000000000E+00 -.314018491737E-15
.816496580928E+00 -.288675134595E+00 .500000000000E+00
.500000000000E+00 .288675134595E+00 .816496580928E+00
.000000000000E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .577350269190E+00 .408248290464E+00
.707106781187E+00 .707106781187E+00 .408248290464E+00
-.577350269190E+00 -.222044604925E-15 .707106781187E+00
.408248290464E+00 -.577350269190E+00 -.222044604925E-15
.277555756156E-15 .577350269190E+00 .408248290464E+00
.707106781187E+00 .000000000000E+00 .000000000000E+00
.000000000000E+00 .000000000000E+00
.500000000000E+00 -.288675134595E+00 .408248290464E+00
.707106781187E+00 .707106781187E+00 .408248290464E+00
.288675134595E+00 -.500000000000E+00 .314018491737E-15
-.181298660735E-15 .256395024851E-15 .100000000000E+01
.155431223448E-14 .384592537277E-15 .407921986653E-15
-.314018491737E-15 .100000000000E+01 .000000000000E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .577350269190E+00 .408248290464E+00
.707106781187E+00 .707106781187E+00 .408248290464E+00
.288675134595E+00 .500000000000E+00 -.628036983474E-15
.362597321469E-15 -.866025403784E+00 -.500000000000E+00
-.199840144433E-14 -.448691293489E-15 -.271947991102E-15
.314018491737E-15 -.500000000000E+00 .866025403784E+00
.000000000000E+00 .000000000000E+00
.000000000000E+00 .577350269190E+00 .408248290464E+00
.707106781187E+00 .707106781187E+00 .408248290464E+00
.288675134595E+00 .500000000000E+00 -.628036983474E-15
.816496580928E+00 -.288675134595E+00 .500000000000E+00
-.155431223448E-14 -.256395024851E-15 .000000000000E+00
.628036983474E-15 .500000000000E+00 .288675134595E+00
.816496580928E+00 .000000000000E+00
.500000000000E+00 -.288675134595E+00 .408248290464E+00
.707106781187E+00 .707106781187E+00 .408248290464E+00
.288675134595E+00 -.500000000000E+00 .707106781187E+00
.408248290464E+00 -.577350269190E+00 .222044604925E-15
.943689570931E-15 .000000000000E+00 -.271947991102E-15
.000000000000E+00 -.133226762955E-14 .577350269190E+00
.408248290464E+00 .707106781187E+00
-
GRAM
20 0
4
2 4
0 -2 4
0 -2 0 4
0 0 -2 0 4
-2 -2 0 0 0 4
0 0 0 0 0 -2 4
0 0 0 0 0 0 -2 4
0 0 0 0 1 -1 0 0 4
0 0 0 0 -1 0 0 0 0 4
0 0 0 0 0 0 0 0 -2 0 4
0 0 0 0 0 0 0 0 0 0 -2 4
1 0 -1 1 1 0 0 -1 1 1 0 -1 4
-1 -1 1 -1 0 0 1 0 1 1 -1 1 0 4
0 0 0 0 0 0 0 0 0 -1 0 0 0 1 4
0 0 0 0 0 0 0 0 -1 1 0 0 1 1 0 4
0 0 1 0 -2 0 0 0 0 0 0 -1 0 0 0 0 4
1 0 0 1 0 0 -1 0 1 0 -1 1 1 0 0 0 1 4
0 0 0 -1 0 1 0 -1 0 0 0 0 1 1 1 0 1 0 4
-1 -1 1 0 -1 1 0 -1 0 1 -1 1 0 1 0 0 1 1 0 4
-
PROPERTIES
INTEGRAL =1
-
NOTES
A laminated lattice.
-
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