The nonexistence of regular near octagons with parameters ( s , t , t 2 , t 3 ) = ( 2 , 24 , 0 , 8 ) Bart

Let S be a regular near octagon with s + 1 = 3 points per line, let t + 1 denote the constant number of lines through a given point of S and for every two points x and y at distance i ∈ {2, 3} from each other, let ti + 1 denote the constant number of lines through y containing a (necessarily unique) point at distance i − 1 from x. It is known, using algebraic combinatorial techniques, that (t2, t3, t) must be equal to either (0, 0, 1), (0, 0, 4), (0, 3, 4), (0, 8, 24), (1, 2, 3), (2, 6, 14) or (4, 20, 84). For all but one of these cases, there is a unique example of a regular near octagon known. In this paper, we deal with the existence question for the remaining case. We prove that no regular near octagons with parameters (s, t, t2, t3) = (2, 24, 0, 8) can exist.