Half of an antipodal spherical design

Abstract

We investigate several antipodal spherical designs on whether we can choose half of the points, one from each antipodal pair, such that they are balanced at the origin. In particular, root systems of type A, D and E, minimal points of Leech lattice and the unique tight 7-design on S 22 are studied. We also study a half of an antipodal spherical design from the viewpoint of association schemes and spherical designs of harmonic index T .1991 Mathematics Subject Classification. 05B30, 05B35.

Classification of Spherical $2$-distance $\{4,2,1\}$-designs by Solving Diophantine Equations

“…More precisely, it might be a difficult problem to choose a point from each antipodal pair of points in a given tight spherical 5-design to get a subset that is a spherical 2-distance {4, 2, 1}-design. Partly motivated by this result, we studied in [7] when a half of an antipodal spherical t-design becomes a spherical 1-design.…”