There is a constant
C
0
C_0
such that all nonabelian finite simple groups of rank
n
n
over
F
q
\mathbb {F}_q
, with the possible exception of the Ree groups
2
G
2
(
3
2
e
+
1
)
^2G_2(3^{2e+1})
, have presentations with at most
C
0
C_0
generators and relations and total length at most
C
0
(
log
n
+
log
q
)
C_0(\log n +\log q)
. As a corollary, we deduce a conjecture of Holt: there is a constant
C
C
such that
dim
H
2
(
G
,
M
)
≤
C
dim
M
\dim H^2(G,M) \leq C\dim M
for every finite simple group
G
G
, every prime
p
p
and every irreducible
F
p
G
{\mathbb F}_p G
-module
M
M
.