The nonexistence of regular near octagons with parameters \((s,t,t_2,t_3)=(2,24,0,8)\)
Summary: Let \({\mathcal S}\) 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 \({\mathcal S}\) and for every two points \(x\) and \(y\) at distance \(i\in\{2,3\}\) from each other, let \(t_i+1\) 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 \((t_2,t_3,t)\) 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 (\((s,t,t_2,t_3)=(2,24,0,8)\) can exist.
scientific article; zbMATH DE number 5827398