A short proof of Totten's classification of restricted linear spaces (Q796823)

Recall that a linear space \((=pairwise\) balanced design with \(\lambda =1)\) is called restricted if it satisfies \((b-v)^ 2\leq v\), where as usual b and v denote the number of lines and points, respectively. In 1976, \textit{J. Totten} classified all restricted linear spaces in his paper in Can. J. Math. 28, 321-333 (1976; Zbl 0308.05021). In the present paper, the author presents a simpler alternative proof of Totten's theorem; one main aspect is the use of techniques from linear algebra.