On the Enumeration of $2–(7,3,\lambda )$ block designs

Abstract

We give the numbers of nonisomorphic $2-(7,3,\lambda )$ block designs for $\lambda =6,7,8,9$. We discuss the method of generation and present statistics concerning automorphism groups and multiple blocks. The $418$ $2-(7,3,6)$ block designs together with the order of their automorphism groups are listed.