Is it possible that one can cover a sphere with 19 equal spherical caps of 30 degrees(i.e. angular radius is 30 degrees)? A table of Neil Sloane suggests it is impossible, but I want to know if anyone could give some theoretical evidence supporting this suggestion.
P.S. L.Fejes Toth gives a quite sharp bound of covering radius in his book "Lagerungen in der ebene auf der Kugel und im Raum".The covering radius $r_n$ is bounded by $\cos{r_n}\leq\frac{1}{\sqrt{3}}\cot{\frac{n\pi}{6(n-2)}}$,where n is the number of spherical caps. But when n=19,the inequality is not strong enough to get what I want.($r_{19}\geq 29.4^{\circ}$)