Abstract
In this paper we establish a construction of Euclidean 9-designs (i.e., the fourth order rotatable designs) on the unit ball. A classical, popular approach for this is to use the corner vectors of the hyperoctahedron such as the vertices, the midpoints of the edges, the barycentres of the faces and so on. As an improvement of this, we propose to use the corner vectors of the hyperoctahedral group, plus their “internally dividing points”. We give a classification of Euclidean 9-designs on two spheres, and several examples of the fourth order optimal rotatable designs in low dimensions.
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