The proper linear spaces on 17 points (Q1302149)

A linear space is an incidence structure \(S=(V,B)\), where \(V\) is a set of points, and \(B\) is a set of subsets of \(V\) called blocks, such that each block contains at least two points and each pair of points lie on a unique block. A linear space is said to be proper if each block contains at least three points and no block has length \(|V|\). The authors classify proper linear spaces on \(17\) points using tactical decompositions, and in particular the tactical decomposition by ordering (TDO) due to \textit{D. Betten} and \textit{M. Braun} [Ann. Discrete Math. 52, 37-43 (1992; Zbl 0769.51004)].