Infinite Families of (q²+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.