Infinite Families of (q^2+1)-Tight Sets of Quadrics with an Automorphism Group PSp(n,q), n=4,6

We present new infinite families of (q²+1)-tight sets of quadrics admitting the symplectic group PSp(n,q), $n=4,6$, as an automorphism group. Our constructions rely on the geometry of Veronese and Grassmann varieties.