  In this paper, we discuss an improvement of an algorithm to search for primes
$p$ and coset-partitions of Z/pZ* that yield Ramsey algebras over Z/pZ. We also
prove an upper bound on the modulus p in terms of the number of cosets. We
have, as a corollary, that there is no prime $p$ for which there exists a
partition of Z/pZ* into 13 cosets that yields a 13-color Ramsey algebra. Thus
A263308(13) = 0.
