  Let $\ell$ be a prime number. We show that the Morita Frobenius number of an
$\ell$-block of a quasi-simple finite group is at most 4 and that the strong
Frobenius number is at most $4|D|^2!$, where D denotes a defect group of the
block. We deduce that a basic algebra of any block of the group algebra of a
quasi-simple finite group over an algebraically closed field of characteristic
$\ell$ is defined over a field with $\ell^a$ elements for some $a \leq 4$. We
derive consequences for Donovan's conjecture. In particular, we show that
Donovan's conjecture holds for $\ell$-blocks of special linear groups.
