... unique regular near octagon with parameters (s, t2 , t3 , t) = (2, 1, 2, 3), namely the Hamming near octagon with three points on each line The unique regular near octagons with parameters (s, t2 ... Theorem 1.1 No regular near octagons exist whose parameters (s, t2 , t3 , t) are equal to (2, 0, 8, 24) Remarks (1) If S is a regular near octagon with parameters (s, t2 , t3 , t) = (2, 0, 8, t), ... octagon with parameters (s, t2 , t3 , t) = (2, 0, 8, 24) would have existed, the eigenvalues of its collinearity graph would have been equal to λ0 = s(t + 1) = 50, λ1 = 13, λ2 = 5, λ3 = −7 and λ4 =...