Known Hyperovals in PG(2,2h)

NameO-PolynomialField
Restriction
Section
Comments
Properties
Hyperconicf(x) = x2None Section 2Available
Translation    (i,h) = 1None Section 2
Segre f(x) = x6h odd Section 2
Glynn Ih odd Section 2
Glynn IIh odd Section 2
Paynef(x) = x1/6+x1/2+x5/6h odd Section 3
Cherowitzoh odd Section 3
Subiacosee commentsNone Section 3
Adelaidesee commentsh even Section 3
Penttila-O'Keefesee commentsh = 5 Section 4

422 mod (2h-1)