  Previous work identifying depth-optimal $n$-channel sorting networks for
$9\leq n \leq 16$ is based on exploiting symmetries of the first two layers.
However, the naive generate-and-test approach typically applied does not scale.
This paper revisits the problem of generating two-layer prefixes modulo
symmetries. An improved notion of symmetry is provided and a novel technique
based on regular languages and graph isomorphism is shown to generate the set
of non-symmetric representations. An empirical evaluation demonstrates that the
new method outperforms the generate-and-test approach by orders of magnitude
and easily scales until $n=40$.
