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

Abstract

We present new infinite families of $(q^2+1)$-tight sets of quadrics admitting the symplectic group ${\rm PSp}(n,q)$, $n=4,6$, as an automorphism group. Our constructions rely on the geometry of Veronese and Grassmann varieties.