Studies on Systems of Six Lines on a Projective Plane over a Prime Field

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.