%0 Journal Article
%T Dual linear spaces generated by a non-Desarguesian configuration
%A James B. Nation
%A Jiajia Y. G. Seffrood
%J Contributions to Discrete Mathematics
%D 2011
%I University of Calgary
%X We describe a method to try to construct non-Desarguesian projective planes of a given finite order using a computer program. If a projective plane of order $n$ exists, then it can be constructed from a dual linear space by a sequence of one-line extensions. This motivates a careful analysis of the failures of Desargues' Law in a dual linear space. Up to isomorphism, there are 105 dual linear spaces generated by a non-Desarguesian configuration with which to start the extension process. A further reduction allows us to limit the number of starting configurations to 15.
%U http://cdm.math.ucalgary.ca/cdm/index.php/cdm/article/view/228