๐”– Bobbio Scriptorium
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Sets of type (m, n) in the affine and projective planes of order nine

โœ Scribed by Tim Penttila; Gordon F. Royle


Publisher
Springer
Year
1995
Tongue
English
Weight
935 KB
Volume
6
Category
Article
ISSN
0925-1022

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๐Ÿ“œ SIMILAR VOLUMES


Parameters for Sets of Type (m, n) in Pr
โœ Mauro Biliotti; Eliana Francot ๐Ÿ“‚ Article ๐Ÿ“… 1999 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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.

On the existence of small quasimultiples
โœ Dieter Jungnickel ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 798 KB

Denote by a(n) and p(n), respectively, the smallest positive integers ,I and p for which an &(2, n, n') and an S,,(2, n + 1, n2 + n + 1) exist. We thus consider the problem of the existence of (nontrivial) quasimultiples of atline and projective planes of arbitrary order n. The best previously known

More on the existence of small quasimult
โœ Alan C. H. Ling ๐Ÿ“‚ Article ๐Ÿ“… 2001 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 112 KB

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

On q24-sets of type (0,q4,q2) in project
โœ A. Maschietti; G. Migliori ๐Ÿ“‚ Article ๐Ÿ“… 1994 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 558 KB

In this paper we investigate qz/4-sets of type (O,q/4,q/2) in projective planes of order q=O(mod4). These sets arise in the investigation of regular triples with respect to a hyperoval. Combinatorial properties of these sets are given and examples in Desarguesian projective planes are constructed.

Hyperovals in the known projective plane
โœ Tim Penttila; Gordon F. Royle; Michael K. Simpson ๐Ÿ“‚ Article ๐Ÿ“… 1996 ๐Ÿ› John Wiley and Sons ๐ŸŒ English โš– 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.

On the Non-existence of Thas Maximal Arc
โœ A. Blokhuis; N. Hamilton; H. Wilbrink ๐Ÿ“‚ Article ๐Ÿ“… 1998 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 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