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Abstract
A dual linear space is a partial projective plane which contains the intersection of every pair of its lines. Every dual linear space can be extended to a projective plane, usually infinite, by a sequence of one line extensions. Moreover, one may describe necessary conditions for the sequence of one line extensions to terminate after finitely many steps with a finite projective plane. A computer program that attempts to construct a finite projective plane from a given dual linear space by a sequence of one line extension has been written by Dr. Nation. In particular, one would like to extend a dual linear space containing a non-Desarguesian configuration to a finite projective plane of non-prime-power order. This dissertation studies the initial dual linear spaces to be used in this algorithm. The main result is that there are 105 non-isomorphic initial dual linear spaces containing the basic non-Desarguesian configuration.
