On the Cardinality of Intersection Sets in Inversive Planes

Intersection sets and blocking sets play an important role in contemporary finite geometry. There are cryptographic applications depending on their construction and combinatorial properties. This paper contributes to this topic by answering the question: how many circles of an inversive plane will be blocked by a d-element set of points that has successively been constructed using a greedy type algorithm? We derive a lower bound for this number and thus obtain an upper bound for the cardinality of an intersection set of smallest size. Defining a coefficient called greedy index, we finally give an asymptotic analysis for the blocking capabilities of circles and subplanes of inversive planes.