 
Name  hadamard_8 
Classification  ncbd8 
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 0/1matrix 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 online encyclopedia of integer
sequences for more information.

 