Legitimate colorings of projective planes

For a projective plane ℙ_n of order n, let κ{script}(ℙ_n) denote the minimum number k, so that there is a coloring of the points of ℙ_n in k colors such that no two distinct lines contain precisely the same number of points of each color. Answering a question of A. Rosa, we show that for all sufficiently large n, 5 ≤κ{script}(ℙ_n) ≤ 8 for every projective plane ℙ_n of order n.