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In this paper, we provide an overview of the SAT+CAS method that combinessatisfiability checkers (SAT solvers) and computer algebra systems (CAS) toresolve combinatorial conjectures, and present new results vis-\`a-vis bestmatrices. The SAT+CAS method is a variant of theDavis$\unicode{8211}$Putnam$\unicode{8211}$Logemann$\unicode{8211}$Loveland$\operatorname{DPLL}(T)$ architecture, where the $T$ solver is replaced by aCAS. We describe how the SAT+CAS method has been previously used to resolvemany open problems from graph theory, combinatorial design theory, and numbertheory, showing that the method has broad applications across a variety offields. Additionally, we apply the method to construct the largest bestmatrices yet known and present new skew Hadamard matrices constructed from bestmatrices. We show the best matrix conjecture (that best matrices exist in allorders of the form $r^2+r+1$) which was previously known to hold for $r\leq6$also holds for $r=7$. We also confirmed the results of the exhaustive searchesthat have been previously completed for $r\leq6$.

The SAT+CAS Method for Combinatorial Search with Applications to Best Matrices