On (q2+q+1)-sets of class [1,m,n]2 in PG(3,q)

Let m,n be two positive integers, a subset K of points of the finite desarguesian 3-dimensional projective space PG(3,q) is of class [1,m,n]2 if every plane of PG(3,q) intersects K either in 1, or m or n points. We shall present a result on (q2+q+1)-sets of points of PG(3,q) of class [1,m,n]2 which implies a characterization of quadric cones of PG(3,q), q odd.