✦ LIBER ✦

On hyperovals in small projective planes

✍ Scribed by Tim Penttila; Gordon F. Royle

Book ID: 112499144
Publisher: Springer
Year: 1995
Tongue: English
Weight: 748 KB
Volume: 54
Category: Article
ISSN: 0047-2468
DOI: 10.1007/bf01222857

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📜 SIMILAR VOLUMES

Hyperovals in the known projective plane

Hyperovals in the known projective planes of order 16

✍ Tim Penttila; Gordon F. Royle; Michael K. Simpson 📂 Article 📅 1996 🏛 John Wiley and Sons 🌐 English ⚖ 382 KB

We construct by computer all of the hyperovals in the 22 known projective planes of order 16. Our most interesting result is that four of the planes contain no hyperovals, thus providing counterexamples to the old conjecture that every finite projective plane contains an oval.

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In [3], W. M. Cherowitzo constructed ovals in all finite Figueroa planes of odd order. Here a class of hyperovals is constructed in the finite Figueroa planes of even order. These hyperovals are inherited from regular hyperovals in the associated desarguesian planes. It is also shown that all Figuer