On 2-designs
The set of \(b\) for which there exists a linear space with \(v\) points and \(b\) lines is studied very sharply, particularly for large \(v\) and for \(v\) of the form \(n^2+n+1\). Interesting is an extremal case: if \(v=n^2+n+1\), \(b=n^22n+1\) the space is obtained from a projective plane replacing one of its lines with a near pencil or a projective plane. Conjectures and problems are given too.
scientific article; zbMATH DE number 3918373