IZhO 2006 Problem 3

Let $m\geq n\geq 4$ be two integers. We call a $m\times n$ board filled with 0's or 1's good if

1. not all the numbers on the board are 0 or 1;

2. the sum of all the numbers in $3\times 3$ sub-boards is the same;

3. the sum of all the numbers in $4\times 4$ sub-boards is the same.

Find all $m,n$ such that there exists a good $m\times n$ board.