General lower bounds on maximal determinants of binary matrices

We give general lower bounds on the maximal determinant of n×n {+1,−1}-matrices, both with and without the assumption of the Hadamard conjecture. Our bounds improve on earlier results of de Launey and Levin (2010) and, for certain congruence classes of nmod4, the results of Koukouvinos, Mitrouli and Seberry (2000). In an Appendix we give a new proof, using Jacobi's determinant identity, of a result of Szöllősi (2010) on minors of Hadamard matrices.