Enumeration of All Simple \(t – (t+7, t+1, 2)\) Designs

We enumerate by computer algorithms all simple \(t-(t+7, t+1, 2)\) designs for \(1 \leq t \leq 5\), i.e., for all possible \(t\). This enumeration is new for \(t \geq 3\). The number of nonisomorphic designs is equal to \(3, 13, 27, 1\) and \(1\) for \(t = 1, 2, 3, 4\) and \(5\), respectively. We also present some properties of these designs, including orders of their full automorphism groups and resolvability.