Selecting Base Points for the Schreier-Sims Algorithm for Matrix Groups

We consider the application of the Schreier-Sims algorithm and its variations to matrix groups defined over finite fields. We propose a new algorithm for the selection of the base points and demonstrate that it both improves the performance of the algorithm for a large range of examples and significantly extends the range of application. In particular, the random Schreier-Sims algorithm, with this enhancement, performs extremely well for almost simple groups.