Linear Programming Bounds for Covering Radius of Spherical Designs

We apply polynomial techniques (i.e., which invole polynomials) to obtain lower and upper bounds on the covering radius of spherical designs as function their dimension, strength, cardinality. In terms inner products we improve due Fazekas Levenshtein propose new bounds. Our approach involves certain signed measures whose corresponding series orthogonal polynomials are positive definite up a (appropriate) degree. The based geometric observation more or less standard in field linear programming techniques.