Amalgams of designs and nets

We present a procedure for amalgamating a net and a collection of designs into a single design. At first this amalgam is just point-regular, but it acquires additional regularities upon imposing restrictions on the ingredients. At its most regular, the amalgam is quasi-symmetric, and designs with the same parameters as those recently constructed by Bracken, McGuire and Ward appear. Along the way we discuss a class of designs generalising Hadamard designs, and we consider the problem of packing projective planes with disjoint line sets into the same point set