CONSTRUCTION OF DESIGNS ON THE 2-SPHERE

Spherical t-designs are Chebyshev-type averaging sets on the d-dimensional unit sphere Sd-1 that are exact for all polynomials of degree at most t. The concept of such designs was introduced by Delsarte, Goethals and Seidel in 1977. The existence of spherical designs for every t and d was proved by Seymour and Zaslavsky in 1984. Although some sporadic examples are known, no general construction has been given. In this paper we give a simple construction of relatively small designs on S2. © 1991, Academic Press Limited. All rights reserved.