Abstract
We prove that nets of order n with small deficiency d relative to n contain no hyperovals unless n is even and d≤2. Secondly, we examine the problems of the existence of r-nets of order n≤8 with ovals or hyperovals; we are able to reduce these problems to a finite number of undetermined orders n. Thirdly, we prove the existence of a set of 7 incomplete mutually orthogonal Latin squares of order n with a hole of size 8 for every integer n≥775. As a corollary, there exists a 9-net of order n with a hyperoval for every n≥775.
Original language | English (US) |
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Pages (from-to) | 53-74 |
Number of pages | 22 |
Journal | Discrete Mathematics |
Volume | 294 |
Issue number | 1-2 |
DOIs | |
State | Published - Apr 28 2005 |
Keywords
- Hyperovals in nets
- Mutually orthogonal Latin squares
- Net
- Ovals in nets
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics