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Design theory is the subfield of combinatorics concerning the existence and construction of highly symmetric arrangements. Finite projective planes, latin squares, and Steiner triple systems are examples of designs.
12
votes
Maximum determinant of $\{0,1\}$-valued $n\times n$-matrices
I shouldn't expect there to be exact results; compare the similar problem
with matrices with entries $\pm1$. For an $n$-by-$n$ matrix with entries $\pm1$
one gets an upper bound for the determinant of …