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

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.