The smallest point sets that meet all generators of H(2n,q2)

It is known that H(2n,q2), n⩾2, does not have ovoids. We improve this result of Thas by showing that the smallest cardinality of a set of points of H(2n,q2) meeting all generators of H(2n,q2) is q2n-2(q3+1). Up to isomorphism there is only one example of this size, and this consists of the points of a cone Sn-2H(2,q2) that do not lie in the vertex Sn-2 of the cone.