The nodes and weights computed with our two-stage algorithm are well suited for applications because of the regular distribution of the nodes. The theoretical results show that for the unit sphere equally weighted quadrature formulae cannot be found except for some special cases. Our weights are, however, very close to being equal.
Finding weights for all numbers of nodes (not only for those coinciding with the dimension of a polynomial space) will be one aim of further research. Another approach might be to inspect other integration measures and thus perhaps find equally weighted quadratures corresponding to these measures. Seymour and Zaslavsky  gave already a hint in this direction.
Our computed facility locations and weights are available at our WWW-server http://www.mathematik.uni-dortmund.de/lsx/fliege/nodes.html.