The Antipode Construction for Sphere Packings

by

J. H. Conway 
Mathematics Department 
Princeton University 
Princeton, New Jersey 08544 

and

N. J. A. Sloane 
Mathematical Sciences Research Center 
AT&T Bell Laboratories 
Murray Hill, New Jersey 07974 

ABSTRACT

A construction for sphere packings is introduced that is
parallel to the ``anticode'' construction for codes.
This provides a simple way to view Vardy's recent 20-dimensional 
sphere packing, and also produces packings in dimensions 22, 44--47
that are denser than any previously known.


A slightly different version of this paper appeared in
Invent. math., 123 (1996), 309-313.

For the full paper see
http://NeilSloane.com/doc/anti.pdf or
http://NeilSloane.com/doc/anti.ps