Ovals and hyperovals in nets

Charles Colbourn, David A. Drake, Wendy Myrvold

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

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 languageEnglish (US)
Pages (from-to)53-74
Number of pages22
JournalDiscrete Mathematics
Volume294
Issue number1-2
DOIs
StatePublished - 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

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