\(2—(22,8,4)\) Designs Have No Blocks of Type \(3\)

Using computer algorithms, we show that in any \(2-(22, 8, 4)\) design, there are no blocks of type \(3\), thus leaving as possible only types \(1\) and \(2\).
Blocks of type \(3\), i.e., those which intersect two others in one point, are eliminated using the algorithms described in our previous paper. It was perhaps the second largest computation ever performed (after the solution to the RSA-129 challenge), requiring more than a century of cpu time.