Bases of schurian antisymmetric coherent configurations and isomorphism test for schurian tournaments

It is known that for any permutation group $G$ of odd order there exists a subset of the permuted set whose stabilizer in $G$ is trivial, and if $G$ is primitive, then there also exists a base of size at most 3. These results are generalized to the coherent configuration of $G$, that is in this case schurian and antisymmetric. This enables us to construct a polynomial-time algorithm for recognizing and isomorphism testing of schurian tournaments (i.e., arc colored tournaments the coherent configurations of which are schurian).