  It has been conjectured that whenever an optimal covering array exists there
is also a uniform covering array with the same parameters and this is true for
all known optimal covering arrays. When used as a test suite, the application
context may have pairs of parameters that must be avoided and Covering arrays
avoiding forbidden edges (CAFE) are a generalization accommodating this
requirement. We prove that there is an arc-transitive, highly symmetric
constraint graph where the unique optimal covering array avoiding forbidden
edges is not uniform. This does not refute the conjecture but it does show that
placing even highly symmetric constraints on covering arrays can force
non-uniformity of optimal arrays.
