How do we place $8n$ objects on a square of size $n\times n$ in a form of grid such that no 4 of them form a rectangle with sides parallel to those of square? Each object occupies exactly one cell in the grid and two objects cannot occupy the same cell. We are given $n\geq 100$.

Example. The following can be a $7\times7$ portion of some large grid (say $200\times200$), where 0 and 1 denote empty and filled cells respectively):

0000111  
0101001
0011100
0110010
1010001
1001010
1100100

What approach one should follow to solve the problem?(source: codechef.com MAY Long challenge)