Spherical t-designs are sets of points on the unit sphere such that the equal weight cubature rule at these points is exact for all spherical polynomials of degrees at most t. As such they can be

regarded as a quasi-Monte Carlo rule for the sphere. Most attention has been focussed on the minimum numbers of points N needed for a spherical t-design.

This talk will focus on the two-sphere and calculation of spherical t-designs with N=t2/2+O(t) and t up to degree 221, their geometrical properties, such as mesh norm, separation, (spherical cap) discrepancy, worst case error and energy. To enable fast generation of point sets we also consider approximate spherical designs.