On the minimum number of points covered by a set of lines in P G (2, q)

Abstract

Segre (Ann Mat Pura Appl 48:1-96, 1959) mentioned that the number of points on a curve which splits into distinct lines on the projective plane over a finite field of order satisfies We see that the upper bound is satisfactory, but the lower one is not for [resp. ] if is odd [resp. even]. We consider the minimum number of points on such a curve of degree , and obtain the complete sequence for every prime power q <= 8.