A New Family of $(q^4+1)$-Tight Sets with an Automorphism Group $F_4(q)$

Abstract

In this paper, we construct a new family of $(q^4+1)$-tight sets in $Q(24,q)$ or $Q^-(25,q)$ according as $q=3^f$ or $q\equiv 2\pmod 3$. The novelty of the construction is the use of the action of the exceptional simple group $F_4(q)$ on its minimal module over $F_q$. The proof relies on a more effective way to decide whether a subset of points of a finite classical polar space is an intriguing set or not.