Exhaustive enumeration of Steiner Triple Systems is not feasible, due to the
the combinatorial explosion of instances.  The next-best hope is to quickly
find a sample that is representative over isomorphism classes.

Stinson's Hill-Climbing algorithm is widely used to produce `random' Steiner
Triple  Systems. It certainly finds a sample quickly, but how close is the

sample thus produced to the `uniform' distribution? In this talk I will
present statistical arguments that the sample is far from uniformly
distributed with respect to the isomorphism classes of the STSs, at least
for v =< 19. In particular, we find that isomorphism classes with a large
number of Pasch configurations are under-represented.

I will also discuss a modification to the standard hill-climbing algorithm
that appears to make the sample found somewhat closer to the uniform
distribution over isomorphism classes in return for a modest increase in
running time.

This is joint work with D. Heap and E. Mendelsohn.