Spherical Designs in Four Dimensions (Extended Abstract)

N. J. A. Sloane (AT&T Shannon Labs, Florham Park, NJ 07932-0971 USA)
R. H. Hardin (227 Glenn Drive, Pataskala, OH 43062 USA)
P. Cara (Department of Mathematics, Vrije Universiteit Brussel Brussels, B-1050 Belgium) 


in Proceedings Information Theory Workshop (Paris, April 2003)


Abstract 

A preliminary report on our investigations into the existence
of spherical t-designs on the unit sphere Omega_4 in 4-dimensional 
Euclidean space. Tables are given of the putatively best t-designs
with up to 100 points. Some general constructions are proposed and
explicit constructions are given for N-point strength t designs
with N=4p and t= min {p-1, 5}, N=6p and t= min {p-1, 7},
and N=12p and t= min {p-1, 11}, for all p >= 1.

For the full version of this extended abstract see
http://www.research.att.com/~njas/doc/paris2.pdf or
http://www.research.att.com/~njas/doc/paris2.ps