  Steiner triple systems (STSs) have been classified up to order 19. Earlier
estimations of the number of isomorphism classes of STSs of order 21, the
smallest open case, are discouraging as for classification, so it is natural to
focus on the easier problem of merely counting the isomorphism classes.
Computational approaches for counting STSs are here considered and lead to an
algorithm that is used to obtain the number of isomorphism classes for order
21: 14,796,207,517,873,771.
