The \(\mathrm {L}_3(4)\) near octagon

In recent work we constructed two new near octagons, one related to the finite simple group \(\mathrm {G}_2(4)\) and another one as a sub-near-octagon of the former. In the present paper, we give a direct construction of this sub-near-octagon using a split extension of the group \(\mathrm {L}_3(4)\). We derive several geometric properties of this \(\mathrm {L}_3(4)\) near octagon, and determine its full automorphism group. We also prove that the \(\mathrm {L}_3(4)\) near octagon is closely related to the second subconstituent of the distance-regular graph on 486 vertices discovered by Soicher (Eur J Combin 14:501–505, 1993).