Arc (projective geometry)

In mathematics, a (k, d)-arc (k, d &ge; 1) of order q in a finite projective plane &pi; (not necessarily Desarguesian) is a set of k points of $$\pi$$ such that each line intersects A in at most d points, and there is at least one line that does intersect A in d points.

Special cases
The number of points k of A is at most qd + d &minus; q. When equality occurs, one speak of a maximal arc.

(q + 1, 2)-arcs are precisely the ovals and (q + 2, 2)-arcs are precisely the hyperovals (which can only occur for even q).