On Linear Representations of Near Hexagons

We discuss linear representations of near polygons in affine spaces. All linear representations of near hexagons in an affine space of orderq ≥ 3 and dimension up to seven are classified. If the dimension of the affine space is at least eight, then the near hexagon necessarily contains a quad of typeT*2(O) and every such quad has a rosette of ovoids. We conjecture that there are no such examples.