  All nonabelian finite simple groups of rank $n$ over a field of size $q$,
with the possible exception of the Ree groups $^2G_2(3^{2e+1})$, have
presentations with at most $80 $ relations and bit-length $O(\log n +\log q)$.
Moreover, $A_n$ and $S_n$ have presentations with 3 generators$,$ 7 relations
and bit-length $O(\log n)$, while $\SL(n,q)$ has a presentation with 7
generators, $2 5$ relations and bit-length $O(\log n +\log q)$.
