Degenerate codon (DC) libraries efficiently address the experimental library-size limitations of directed evolution by focusing diversity toward the positions and toward the amino acids (AAs) that are most likely to generate hits; however, manually constructing DC libraries is challenging, error prone and time consuming. This paper provides a dynamic programming solution to the task of finding the best DCs while keeping the size of the library beneath some given limit, improving on the existing integer-linear programming formulation. It then extends the algorithm to consider multiple DCs at each position, a heretofore unsolved problem, while adhering to a constraint on the number of primers needed to synthesize the library. In the two library-design problems examined here, the use of multiple DCs produces libraries that very nearly cover the set of desired AAs while still staying within the experimental size limits. Surprisingly, the algorithm is able to find near-perfect libraries where the ratio of amino-acid sequences to nucleic-acid sequences approaches 1; it effectively side-steps the degeneracy of the genetic code. Our algorithm is freely available through our web server and solves most design problems in about a second
