A new sphere packing in 20-dimensional Euclidean space

It is well-known since the celebrated work of Shannon (1948) that the design of efficient transmission codes for bandlimited channels with additive white Gaussian noise is equivalent to the problem of constructing dense arrangements of nonoverlapping spheres in R/sup n/. We describe a new nonlattice sphere packing /spl Tscr/20/spl sub/R/sup 20/ which is denser than any previously known sphere packing in R/sup 20/. The properties of /spl Tscr/20 are investigated, and several alternative representations of the new packing are presented. One of these was recognized by Conway and Sloane (see 2nd Ed., Springer-Verlag, New York, 1993) as the first example of the so-called antipode packings, leading them to the discovery of new densest-known sphere packings also in dimensions 22 and 44-47.