Linear spaces with at most 12 points

Abstract

The 28,872,973 linear spaces on 12 points are constructed. The parameters of the geometries play an important role. In order to make generation easy, we construct possible parameter sets for geometries first (purely algebraically). Afterwards, the corresponding geometries are tried to construct. We define line types, point types, point cases, and also refined line types. These are the first three steps of a general decomposition according to the parameters which we call TDO. The depth of parameter precalculation can be varied, thereby obtaining a handy tool to react in a flexible way to different grades of difficulty of the problem. © 1999 John Wiley & Sons, Inc. J Combin Designs 7: 119–145, 1999