Dense near octagons with four points on each line, II

Abstract

Abstract This is the second paper in a series of three dealing with the classification of the dense near octagons of order (3, t). In [B. De Bruyn, Dense near octagons with four points on every line, I. Ann. Combin., to appear.], we determined all dense near octagons of order (3, t) with a big hex. In the present paper, we will obtain a partial classification of the valuations of the dense near hexagons of order (3, t). We shall use this classification to obtain some classification results regarding dense near polygons of order (3, t) containing exceptional hexes. The classification of the valuations will be used in [B. De Bruyn, Dense near octagons with four points on every line, III. Preprint.] to show that almost all dense near octagons of order (3, t) have a big hex.