The nonexistence of certain tight spherical designs
The nonexistence of certain tight spherical designs
In this paper, the nonexistence of tight spherical designs is shown in some cases left open to date. Tight spherical 5-designs may exist in dimension $n=(2m+1)^{2}-2$, and the existence is known only for $m=1,2$. In the paper, the existence is ruled out under a certain arithmetic condition on the integer …