Finite Linear Spaces With Four More Lines Than Points

Abstract

In 1948, de Bruijn and Erdős proved that every finite linear space on \(v\) points and with \(6\) lines fulfils the inequality \(b \geq v\), and the equality holds if the linear space is a (possibly degenerate) projective plane. This result led to the problem of classifying finite linear spaces on \(v\) points and with \(b = v + s\) lines, \(s \geq 1\). This paper contains the classification of finite linear spaces on \(v\) points and with \(b = v + 4\) lines.