✦ LIBER ✦

Hyperovals in the known projective planes of order 16

✍ Scribed by Tim Penttila; Gordon F. Royle; Michael K. Simpson

Publisher: John Wiley and Sons
Year: 1996
Tongue: English
Weight: 382 KB
Volume: 4
Category: Article
ISSN: 1063-8539
DOI: 10.1002/(sici)1520-6610(1996)4:1<59::aid-jcd6>3.0.co;2-z

No coin nor oath required. For personal study only.

✦ Synopsis

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.

📜 SIMILAR VOLUMES

Intersections of Hyperconics in Projecti

Intersections of Hyperconics in Projective Planes of Even Order

✍ Aiden A. Bruen; James M. McQuillan 📂 Article 📅 2001 🏛 Elsevier Science 🌐 English ⚖ 204 KB

We show how to lift the even intersection equivalence relation from the hyperovals of PG(2, 4) to an equivalence relation amongst sets of hyperconics in "PG(2, F ). Here, F is any "nite or in"nite "eld of characteristic two that contains a sub"eld of order 4, but does not contain a sub"eld of order

I-Transitive Ovals in Projective Planes

I-Transitive Ovals in Projective Planes of Odd Order

✍ Maria Rosaria Enea; Gábor Korchmáros 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 202 KB

Let be a projective plane of odd order n containing an oval ⍀. We give a classification of collineation groups of which fix ⍀ and act transitively on the set I I of all internal points of ⍀.

On the Non-existence of Thas Maximal Arc

On the Non-existence of Thas Maximal Arcs in Odd Order Projective Planes

✍ A. Blokhuis; N. Hamilton; H. Wilbrink 📂 Article 📅 1998 🏛 Elsevier Science 🌐 English ⚖ 91 KB

In this paper it is shown that given a non-degenerate elliptic quadric in the projective space PG(2n -1, q), q odd, then there does not exist a spread of PG(2n -1, q) such that each element of the spread meets the quadric in a maximal totally singular subspace. An immediate consequence is that the c

The nonexistence of projective planes of

The nonexistence of projective planes of order 12 with a collineation group of order 8

✍ Kenzi Akiyama; Chihiro Suetake 📂 Article 📅 2008 🏛 John Wiley and Sons 🌐 English ⚖ 183 KB

## Abstract In this article, we prove that there does not exist a symmetric transversal design ${\rm STD}\_2[12;6]$ which admits an automorphism group of order 4 acting semiregularly on the point set and the block set. We use an orbit theorem for symmetric transversal designs to prove our result. A

Parameters for Sets of Type (m, n) in Pr

Parameters for Sets of Type (m, n) in Projective Planes of Prime Power Order

✍ Mauro Biliotti; Eliana Francot 📂 Article 📅 1999 🏛 Elsevier Science 🌐 English ⚖ 88 KB

A set S of k points in a projective plane of order q is of type (m, n) if each line meets S in either m or n points. The parameters are standard if q=a 2 for a=n&m. In this note we give a method for determining all admissible nonstandard parameters for a given m and q a prime power.

More on the existence of small quasimult

More on the existence of small quasimultiples of affine and projective planes of arbitrary order

✍ Alan C. H. Ling 📂 Article 📅 2001 🏛 John Wiley and Sons 🌐 English ⚖ 112 KB

## Abstract The functions __a(n)__ and __p(n)__ are defined to be the smallest integer λ for which λ‐fold quasimultiples affine and projective planes of order __n__ exist. It was shown by Jungnickel [J. Combin. Designs 3 (1995), 427–432] that __a(n),p(n)__ < __n__^10^ for sufficiently large __n__.