Summary
All ovals in the Desarguesian plane of order 16 are determined. Up to equivalence under the collineation group of the plane there are exactly two classes of ovals. In the first class an oval consists of the points of a conic together with its nucleus. There is exactly one other class of ovals and the collineations fixing an oval in this class are transitive on the 18 points of the oval.
Article PDF
Similar content being viewed by others
References
M. Hall jr. - J. D. Swift -R. J. Walker,Uniqueness of the projective plane of order eight, Math. Tables and Other Aids to Computation,10 (1956), pp. 186–194.
M. Hall jr.,Combinatorial Theory, Blaisdell Publishing Company, 1967.
B. Segre,Introduction to Galois geometries, Memoirs of the Accademia Nazionale dei Lincei (1967), Series 81, volume 8, Section 1a, pp. 135–236.
Author information
Authors and Affiliations
Additional information
Dedicated to ProfessorBeniamino Segre on the occasion of his 70th birthday
Entrata in Redazione il 24 maggio 1973.
This research was supported in part by ONR Contract NOO14-67-A-0094-0010 and NSF Grant GP 36230X.
Rights and permissions
About this article
Cite this article
Hall, M. Ovals in the Desarguesian plane of order 16. Annali di Matematica 102, 159–176 (1975). https://doi.org/10.1007/BF02410604
Issue Date:
DOI: https://doi.org/10.1007/BF02410604