A new near octagon and the Suzuki tower
Anurag Bishnoi, Bart De Bruyn

TL;DR
This paper introduces a new near octagon of order (2,10), explores its automorphism group, and uses it to geometrically construct certain strongly regular graphs within the Suzuki tower, also discovering a smaller near octagon.
Contribution
It constructs a novel near octagon of order (2,10), analyzes its automorphism group, and provides geometric constructions of the G_2(4)-graph and Suzuki graph.
Findings
Constructed a near octagon of order (2,10) with automorphism group G_2(4):2.
Embedded 416 copies of the Hall-Janko near octagon within it.
Discovered a new near octagon of order (2,4) as a subgeometry.
Abstract
We construct and study a new near octagon of order which has its full automorphism group isomorphic to the group and which contains copies of the Hall-Janko near octagon as full subgeometries. Using this near octagon and its substructures we give geometric constructions of the -graph and the Suzuki graph, both of which are strongly regular graphs contained in the Suzuki tower. As a subgeometry of this octagon we have discovered another new near octagon, whose order is .
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