The SAT+CAS paradigm and the Williamson conjecture

Abstract

We employ tools from the fields of symbolic computation and satisfiability checking---namely, computer algebra systems and SAT solvers---to study the Williamson conjecture from combinatorial design theory and increase the bounds to which Williamson matrices have been enumerated. In particular, we completely enumerate all Williamson matrices of orders divisible by 2 or 3 up to and including 70. We find one previously unknown set of Williamson matrices of order 63 and construct Williamson matrices in every even order up to and including 70. This extended abstract outlines a preprint currently under submission [4].