General Lower Bounds on Maximal Determinants of Binary Matrices

Richard P. Brent, Judy-anne H. Osborn

Abstract


We give general lower bounds on the maximal determinant of $n \times n$ $\{+1,-1\}$-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 $n \bmod 4$, 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.


Keywords


{+-1}-matrices; lower bounds; maximal determinant; D-optimal designs; Hadamard matrices

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