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%I A352348 #20 Jun 04 2023 01:45:31
%S A352348 1,2,2,16,16,125,128,4096,4096,59049,59049,2985984,2985984,62748517
%N A352348 Maximum determinant of n X n matrix composed of {-1, 0, 1} with pairwise orthogonal rows.
%C A352348 a(n) >= a(m)*a(n-m) for any m < n.
%C A352348 a(n) <= A003433(n), a bound achieved if the orthogonality requirement is dropped.
%C A352348 If there exists an order n Hadamard matrix, then a(n) = A003433(n) = n^(n/2).
%C A352348 For n == 2 (mod 4), if there exists an order n conference matrix (cf. A000952), then a(n) = (n-1)^(n/2). In particular, a(18) = 118587876497.
%H A352348 Arun et al., <a href="https://mathoverflow.net/q/418009">Reference request: maximal determinant of matrices with pairwise orthogonal rows and entries in {1, 0, -1}</a>, MathOverflow, 2022.
%H A352348 Wikipedia, <a href="https://en.wikipedia.org/wiki/Conference_matrix">Conference matrix</a>.
%H A352348 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hadamard_matrix">Hadamard matrix</a>.
%Y A352348 Cf. A000952, A003432, A003433.
%K A352348 hard,more,nonn
%O A352348 1,2
%A A352348 _Max Alekseyev_, Mar 12 2022
%E A352348 a(11)-a(14) from _Max Alekseyev_, May 20 2023