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A projective plane of order 16

โœ Scribed by Peter Lorimer

Publisher
Elsevier Science
Year
1974
Tongue
English
Weight
735 KB
Volume
16
Category
Article
ISSN
0097-3165

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๐Ÿ“œ SIMILAR VOLUMES

Hyperovals in the known projective plane
Hyperovals in the known projective planes of order 16
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.

The nonexistence of ovals in a projectiv
The nonexistence of ovals in a projective plane of order 10
โœ C.W.H. Lam; L. Thiel; S. Swiercz; J. McKay ๐Ÿ“‚ Article ๐Ÿ“… 1983 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 325 KB

This paper reports the result of a computer search which show s that there is no oval in a projective plane of order 10. It gives a brief description of the search method as well as a brief survey of other possible configurations in a plane of order 10.

Translation Laguerre Planes of Order 16
Translation Laguerre Planes of Order 16
โœ D.G. Glynn; G.F. Steinke ๐Ÿ“‚ Article ๐Ÿ“… 1993 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 434 KB

Translation Laguerre planes of order 16 are investigated, and a related search is carried out for translation ovals in the eight translation planes of order 16 and for certain collections of such ovals called 2-pencils. Although in some of these planes there are considerably more translation hyperov