On the existence of certain symmetric affine resolvable designs (Q802561)

A symmetric affine resolvable design \(H_ m(\mu)\) is a set of \(\mu m^ 2\) points and \(\mu\) m parallel classes of m blocks, each with \(\mu\) m points, such that two non-parallel blocks intersect in \(\mu\) points, and the dual design also has these properties. The authors give a detailed analysis of an \(H_ 3(\mu)\), particularly discussing triples of blocks whose intersection has \(\mu\) elements. They give a construction of at least two non-isomorphic \(H_ 3(3\mu)\) designs from two \(H_ 3(\mu)\) designs. As an example, they construct four non-isomorphic \(H_ 3(6)\) designs.