Presentations of finite simple groups: a computational approach

All finite simple groups of Lie type of rank n over a field of size q, with the possible exception of the Ree groups 2G₂ (q), have presentations with at most 49 relations and bit-length O (log n + log q). Moreover, An and Sn have presentations with 3 generators; 7 relations and bit-length O (log n), while SL (n, q) has a presentation with 6 generators, 25 relations and bit-length O (log n + log q).