  We establish new lower bounds for $28$ classical two and three color Ramsey
numbers, and describe the heuristic search procedures we used. Several of the
new three color bounds are derived from the two color constructions;
specifically, we were able to use $(5,k)$-colorings to obtain new
$(3,3,k)$-colorings, and $(7,k)$-colorings to obtain new $(3,4,k)$-colorings.
Some of the other new constructions in the paper are derived from two
well-known colorings: the Paley coloring of $K_{101}$ and the cubic coloring of
$K_{127}$.
