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Hard  hadamard_8

Problem typehadamard
DescriptionMaximize determinant of 8 times 8 binary matrix
Objective sensemax
Variables64  (64 binary, 0 general integer, 0 continuous)
Nonlinear variables64
Nonlinear constraints0
Linear nonzeros0
Nonlinear nonzeros40320
Download hadamard_8.pip.gz
Best known solution
Best known objective56
Best known bound56
OriginatorMarc Pfetsch
FormulatorMarc Pfetsch
DonatorMarc Pfetsch
Additional informationLet a(n) be the maximal determinant of a 0/1-matrix of size n by n. Hadamard proved that a(n) ≤ 2(-n) (n+1)((n+1)/2). A Hadamard matrix attains this bound. The Hadamard conjecture states that this is the case if and only if n+1 is 1 or 2 or a multiple of 4. The values of a(n) for small n are known. See the on-line encyclopedia of integer sequences for more information.

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