The main purpose of this paper is to show the nonexistence of tight Euclidean 9-designs on 2 concentric spheres in Rn if n ≥ 3. This in turn implies the nonexistence of minimum cubature formulas of degree 9 (in the sense of Cools and Schmid) for any spherically symmetric integrals in Rn if n ≥ 3.
"Tight 9-designs on two concentric spheres." J. Math. Soc. Japan 63 (4) 1359 - 1376, October, 2011. https://doi.org/10.2969/jmsj/06341359