I am doing a worst case scenario analysis of the theoretically most inconsistent ranking where   I need the solution of the following problem.

A matrix of $k$ rows and $n$ columns is filled with the numbers $1,2,\ldots,k$ such that the following conditions are satisfied:
 
1. Every column contain all the numbers form 1 to $k$ ***without repetition***.
2. The variance of the elements of each row is calculated. The matrix is filled in such a way that the total sum $S_{kn}$ of the variance of each row is maximized.

**Questions**:

1. What is the representation of the maximum value of $S_{kn}$ in a closed form in terms of  $k$ and $n$? 
2. Is there an algorithm to fill the matrix such that $S_{kn}$ is maximized? 
3. If ***repetition*** is allowed, what would be the answers for the above two questions.