Known Hyperovals in PG(2,2^h)

Name	O-Polynomial	Field Restriction	Section Comments	Properties
Hyperconic	f(x) = x2	None	Section 2	Available
Translation	(i,h) = 1	None	Section 2
Segre	f(x) = x6	h odd	Section 2
Glynn I		h odd	Section 2
Glynn II		h odd	Section 2
Payne	f(x) = x1/6+x1/2+x5/6	h odd	Section 3
Cherowitzo		h odd	Section 3
Subiaco	see comments	None	Section 3
Adelaide	see comments	h even	Section 3
Penttila-O'Keefe	see comments	h = 5	Section 4

⁴²2 mod (2^h-1)