 
Name  hadamard_7 
Classification  ncbd7 
Problem type  hadamard 
Description  Maximize determinant of 7 times 7 binary matrix 
 
Objective sense  max 
Variables  49 (49 binary, 0 general integer, 0 continuous) 
Nonlinear variables  49 
Constraints  0 
Nonlinear constraints  0 
Linear nonzeros  0 
Nonlinear nonzeros  5040 
 
Download  hadamard_7.pip.gz 
Best known solution  
Best known objective  32 
Best known bound  32 
 
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.

 