A generalization of the Haemers–Mathon bound for near hexagons

Abstract

The Haemers–Mathon bound states that $t\le s^3+t_2(s^2-s+1)$ for any finite regular near hexagon with parameters $(s,t,t_2)$, $s\ge 2$. In this paper, we generalize this bound to arbitrary finite near hexagons with an order. The obtained inequality involves the orders of the quads through a given line.