Constructions of Φp-Optimal Rotatable Designs on the Ball

We discuss two fundamental methods for constructing Φp-optimal approximate designs of order 3 on the unit ball. One construction is based on the theory of harmonic polynomials invariant under the Weyl group of type B, and another uses statistical tools such as block designs and orthogonal arrays. The paper provides a systematic treatment of a group-theoretic approach for constructing such designs, which has been traditionally used by Gaffke and Heiligers (1995a, b, c) and other researchers in design of experiments. © 2014, Indian Statistical Institute.