Small point sets that meet all generators of Q(2n,p), p>3 prime

It was shown recently that Q(6,q), q>3, q a prime has no ovoids. We improve this result by showing that the smallest cardinality of a set of points of Q(6,q), q>3 prime, meeting all generators of Q(6,q) is q3+q. Up to isomorphism there is only one example of this size. At last, we generalize this result to Q(2n,q).