Association Schemes on the Sets of Lines of Regular Near Hexagons

Abstract

We investigate the conditions under which an association scheme exists on the set of lines of a regular near hexagon with quads of order $(s,t_2)$ passing through every two points at distance $2$. Specifically, we determine all regular near hexagons admitting such an association scheme when $s\ge t_2$, while the case $t^2>s$ remains open.