Unitary Designs with a Common Collection of Blocks

It is well known that one can construct a family of \(\frac{q^2 – q}{2}\) Miquelian inversive planes on the same point set such that any two share exactly the blocks through a fixed point. Further, Ebert [10] has shown that this family can be augmented for even \(q\) by adding some Suzuki-Tits inversive planes. We wish to apply the method of Ebert combined with a technique from Dover [6] to obtain a family of unitals which have the same property.