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 each cell can occupy at most one object. We are given $n\geq 100$.

What approach one should follow to solve the problem?

Example (F and E denotes filled and empty cells respectively):

Consider the following 3X3 portion of some large grid (say 200X200)

F F F

F E E

F E E