  We present accurate upper and lower bounds for the covering numbers, with
explicit constants, of the unit ball for two general classes of Reproducing
Kernel Hilbert Space (RKHS) on the unit sphere of $\mathbb{R}^{d+1}$. In both
classes, the RKHS is generated by an isotropic continuous positive definite
kernel. The upper and lower bounds we present carry precise information about
the asymptotic constants, depending on the dimension of the sphere and the
monotonic behavior of the Schoenberg/Fourier coefficients of the isotropic
kernel.
