By Nicolaas Govert de Bruijn and Paul Erdős. Proceedings of the Koninklijke Nederlandse Akademie van Wetenschappen51,1277–1279 (also Indagationes Mathematicae10,421–423). Primary scan: users.renyi.hu/~p_erdos/1948-01.pdf
Theorem1 gives the finite unique-pair line-count bound and identifies the near-pencil and projective-plane equality configurations.