401 and beyond: improved bounds and algorithms for the Ramsey algebra search

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.