Extending partial projective planes (Q1721743)

In this paper, the author explains an idea to construct finite projective planes using computational methods. The idea is to start from a non-Desarguesian configuration in a semiplane, and to extend this semiplane by adding lines and intersection points, taking care that the final number of points and lines equals the number of points and lines of a projective plane of the desired order. When the semiplane is maximal, in the sense that it cannot be extended to a projective plane (of a desired order), the starting configuration will not yield a projective plane. Four cases of constructed maximal semiplanes are listed, taken from [the author and \textit{J. Y. G. Seffrood}, Contrib. Discrete Math. 6, No. 1, 98--141 (2011; Zbl 1327.51011)].