Geodesic
Schemes of relations of the finite projective plane, and their extensions
Algebra i analiz, Tome 21 (2009) no. 1, pp. 90-132.

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There are several schemes (coherent configurations) associated with a finite projective plane $\mathcal P$. In the paper, a new scheme is constructed, which, in a sense, contains all of them. It turns out that this scheme coincides with the 2-extension of the nonhomogeneous scheme of $\mathcal P$, and is uniquely determined up to similarity by the order $q$ of $\mathcal P$. Moreover, for $q\ge 3$ the rank of the scheme does not depend on $q$ and equals 416. The results obtained have interesting applications in the theory of multidimensional extensions of schemes and similarities.
Keywords: projective plane, Galois plane, scheme, graph. 
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S. A. Evdokimov; I. N. Ponomarenko. Schemes of relations of the finite projective plane, and their extensions. Algebra i analiz, Tome 21 (2009) no. 1, pp. 90-132. http://geodesic.mathdoc.fr/item/AA_2009_21_1_a3/

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