In geometry, a unital is a set of n3 + 1 points arranged into subsets of size n + 1 so that every pair of distinct points of the set are contained in exactly one subset.[a] This is equivalent to saying that a unital is a 2-(n3 + 1, n + 1, 1) block design. Some unitals may be embedded in a projective plane of order n2 (the subsets of the design become sets of collinear points in the projective plane). In this case of embedded unitals, every line of the plane intersects the unital in either 1 or n + 1 points. In the Desarguesian planes, PG(2,q2), the classical examples of unitals are given by nondegenerate Hermitian curves. There are also many non-classical examples. The first and the only known unital with non prime power parameters, n=6, was constructed by Bhaskar Bagchi and Sunanda Bagchi.[1] It is still unknown if this unital can be embedded in a projective plane of order 36, if such a plane exists.
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