Numerical verification methods for spherical t-designs

The construction of spherical t-designs with (t + 1)2points on the unit sphere S2in ℝ3can be reformulated as an underdetermined system of nonlinear equations. This system is highly nonlinear and involves the evaluation of a degree t polynomial in (t+1)4arguments. This paper reviews numerical verification methods using the Brouwer fixed point theorem and Krawczyk interval operator for solutions of the underdetermined system of nonlinear equations. Moreover, numerical verification methods for proving that a solution of the system is a spherical t-design are discussed.