hadamard_8
POLIPlibrary for polynomially constrained
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hadamard_8| Name | hadamard_8 |
| Classification | nc|b|d8 |
| Problem type | hadamard |
| Description | Maximize determinant of 8 times 8 binary matrix |
| Objective sense | max |
| Variables | 64 (64 binary, 0 general integer, 0 continuous) |
| Nonlinear variables | 64 |
| Constraints | 0 |
| Nonlinear constraints | 0 |
| Linear nonzeros | 0 |
| Nonlinear nonzeros | 40320 |
| Download | hadamard_8.pip.gz |
| Best known solution | |
| Best known objective | 56 |
| Best known bound | 56 |
| Originator | Marc Pfetsch |
| Formulator | Marc Pfetsch |
| Donator | Marc Pfetsch |
| References | |
| Links | |
| Additional information | Let 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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