Odd q
In a finite projective plane of odd order q, no sets with more points than q + 1, no three of which are collinear, exist, as first pointed out by Bose in a 1947 paper on applications of this sort of mathematics to statistical design of experiments.
Due to Segre's theorem (Segre 1955), every oval in PG(2, q) with q odd, is projectively equivalent to a nonsingular conic in the plane.
This implies that, after a possible change of coordinates, every oval of PG(2, q) with q odd has the parametrization :
Read more about this topic: Oval (projective Plane)
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