  We use heuristic algorithms to find terraces for small groups. We show that
Bailey's Conjecture (that all groups other than the non-cyclic elementary
abelian 2-groups are terraced) holds up to order 511, except possibly at orders
256 and 384. We also show that Keedwell's Conjecture (that all non-abelian
groups of order at least 10 are sequenceable) holds up to order 255, and for
the groups $A_6$, $S_6$, $PSL(2,q_1)$ and $PGL(2, q_2)$ where $q_1$ and $q_2$
are prime powers with $3 \leq q_1 \leq 11$ and $3 \leq q_2 \leq 8$. A
sequencing for a group of a given order implies the existence of a complete
latin square at that order. We show that there is a sequenceable group for each
odd order up to 555 at which there is a non-abelian group. This gives 31 new
orders at which complete latin squares are now known to exist, the smallest of
which is 63. In addition, we consider terraces with some special properties,
including constructing a directed $T_2$-terrace for the non-abelian group of
order 21 and hence a Roman-2 square of order 21 (the first known such square of
odd order). Finally we report the total number terraces and directed terraces
for groups of order at most 15.
