The small linear spaces

All finite linear spaces with a small number v of points are classified, up to isomorphism. The cases v<10 were originally classified using only paper and pencil. The bigger cases really need the aid of a computer, and the results for v=10,11,12 are due to Betten.

v Isomorphism types
0 1
1 1
2 1
3 2
4 3
5 5
6 10
7 24
8 69
9 384
10 5.250
11 232.929
12 28.872.973

Betten also classified the proper linear spaces with v=17,18 points, so all proper linear spaces with v<19 are known. The case v=19 is much harder, for example v=19 includes the classification of all Steiner triple systems on v=19 points.


Contributed by Hauke Klein
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