  Several methods for generating random Steiner triple systems (STSs) have been
proposed in the literature, such as Stinson's hill-climbing algorithm and
Cameron's algorithm, but these are not yet completely understood. Those
algorithms, as well as some variants, are here assessed for STSs of both small
and large orders. For large orders, the number of occurrences of certain
configurations in the constructed STSs are compared with the corresponding
expected values of random hypergraphs. Modifications of the algorithms are
proposed.
