On the number of lines in planar spaces

Abstract

SupposeS is a planar space withv>4 points and letq be the positive real number such thatv=q 3+q2+q+1. Assuming a weak non-degeneracy condition, we shall show thatS has at least (q2+1)(q2+q+1) lines with equality iffq is a prime power andS=PG(3,q).

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Metsch, K. On the number of lines in planar spaces. Combinatorica 15, 105–110 (1995). https://doi.org/10.1007/BF01294462

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Mathematics Subject Classification (1991)

  • 05 A 20
  • 05 B 25