Ovoids
When one takes as points the points of an ovoid in PG(3,q), with q a prime power, and as blocks the planes that are not tangent to the ovoid, one finds a design.
Inversive planes that arise in this way are said to be egglike. Dembowksi proved that when n is even, every inversive plane is egglike (and thus n is a power of 2). It is not known to be true when n is odd.
Read more about this topic: Inversive Plane