Ovoids of PG(3,16) are elliptic quadrics
The authors prove that elliptic quadrics are the only ovoids in projective 3-space PG(3,16) over GF(16). Uniqueness of the inversive plane of order 16 is one of the consequences of this result. The proof is based on a result of \textit{D. G. Glynn} and the second author [A plane representation of ovoids, to appear] which expresses the existence of an ovoid in PG(3,1) in terms of a set of q ovals in PG(2,q). The ovals in PG(2,16) have been determined by \textit{M. Hall} jun. [Ann. Mat. Pura Appl., IV. Ser. 102, 159-176 (1975; Zbl 0313.50013)], cp. also the authors [Eur. J. Comb. 12, 51-60 (1991)], and the authors exclude all ovals which are not conics (with a little help from a small computer).
scientific article; zbMATH DE number 4161556
scientific article