t-Designs with the number of blocks close to the Fisher type lower bound

Abstract

It is shown that, for any given pair of positive integers e and c, there are only finitely many non-trivial 2e-$(v,k,\lambda )$ designs where the number of blocks b is equal to $\left(\begin{array}{c}\hfill v\hfill \\ \hfill e\hfill \end{array}\right)+c$.