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Unitary Designs with a Common Collection of Blocks

Jeremy M. Dover1
1 Department of Mathematics Moravian College, Bethlehem, PA 18018

Abstract

It is well known that one can construct a family of q2q2 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.