Abstract
In this paper, we prove the existence of a spherical t-design formed by adding extra points to an arbitrarily given point set on the sphere and, subsequently, deduce the existence of nested spherical designs. Estimates on the number of required points are also given. For the case that the given point set is a spherical t1-design such that t1<t and the number of points is of optimal order t1d, we show that the upper bound of the total number of extra points and given points for forming nested spherical t-design is of order t2d+1. A brief discussion concerning the optimal order in nested spherical designs is also given.
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