Let $A(k,n)$ be the set of $\{0,1\}$ matrices of order $n$ with all their line sums equal to $k$. 

Conjecture number 5 on the list from [Minc's book][1], attributed to Ryser, says that if $A(k,n)$ contains incidence matrices of symmetric $(n,k,\lambda)$-designs, then the minimum permanent on $A(k,n)$ is attained at one of theses incidence matrices.

It's also number 8 on [Zhan's recent list][2] of open problems in matrix theory. As one can see there, it has been verified by Wanless up to $n=12$ but not beyond.

I wonder if, given the recent progress on permanents, there is more known now about this conjecture?


  [1]: http://books.google.co.il/books/about/Encyclopedia_of_Mathematics_and_Its_Appl.html?id=gnT2LCvciqUC&redir_esc=y
  [2]: http://math.ecnu.edu.cn/~zhan/papers/ZhanICCM.pdf