Inversive plane

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An inversive plane is a 3 − (n² + 1,n + 1,1) − design. By definition it is always a Steiner system.

[edit] 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 3 − (q² + 1,q + 1,1) − 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 a power of 2). It is not known to be true when n is odd.