On a class of finite linear spaces with few lines (Q1406556)

It has been shown by \textit{N. G. de Bruijn} and \textit{P. Erdős} [Indag. Math. 10, 421-423 (1948); see also Proc. Akad. Wet. Amsterdam 51, 1277-1279 (1948; Zbl 0032.24405)] that a finite linear space has at least as many lines as points, with equality if and only if it is a projective plane or a near-pencil. The author characterizes the finite linear spaces such that the difference between the number \(b\) of lines and the number \(v\) of points is less or equal to the minimum point degree. He finds 10 infinite families and 6 sporadic examples. The author also mentions different known characterization results for finite linear spaces with a bound on \(b-v\).