Geodesic
Studies on Systems of Six Lines on a~Projective Plane over a~Prime Field
Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 2, pp. 140-151

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A simple six-line arrangement on a projective plane is obtained by a system of six labelled lines $L_1,L_2,\ldots,L_6$ with the conditions; (1) they are mutually different and (2) no three of them intersect at a point. We add the condition that (3) there is no conic tangent to all the lines. The main subject of this paper is to treat such arrangements on a projective plane over a finite prime field.
Keywords: projective plane, finite prime field, quadratic residue. 
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Jiro Sekiguchi. Studies on Systems of Six Lines on a~Projective Plane over a~Prime Field. Žurnal Sibirskogo federalʹnogo universiteta. Matematika i fizika, Tome 1 (2008) no. 2, pp. 140-151. http://geodesic.mathdoc.fr/item/JSFU_2008_1_2_a3/