Association Schemes on the Sets of Lines of Regular Near Hexagons

Bart De Bruyn1
1 Department of Pure Mathematics and Computer Algebra, Ghent University, Krijgslaan 281 (S22), B-9000 Gent, Belgium,

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 \(s \geq t_2\), while the case \(t^2 > s\) remains open.