Hyperovals in the Known Projective Planes of Order 16

Tim Penttila; Gordon Royle; M.K. Simpson

doi:10.1002/(SICI)1520-6610(1996)4:1<59::AID-JCD6>3.0.CO;2-Z

Hyperovals in the Known Projective Planes of Order 16

Tim Penttila, Gordon Royle, M.K. Simpson

Graduate Research School

Research output: Contribution to journal › Article › peer-review

31 Citations (Scopus)

Abstract

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. (C) 1996 John Wiley & Sons, Inc.

Original language	English
Pages (from-to)	59-65
Journal	Journal of Combinatorial Designs
Volume	4
DOIs	https://doi.org/10.1002/(SICI)1520-6610(1996)4:1<59::AID-JCD6>3.0.CO;2-Z
Publication status	Published - 1996

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10.1002/(SICI)1520-6610(1996)4:1<59::AID-JCD6>3.0.CO;2-Z

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title = "Hyperovals in the Known Projective Planes of Order 16",

abstract = "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. (C) 1996 John Wiley & Sons, Inc.",

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AU - Simpson, M.K.

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AB - 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. (C) 1996 John Wiley & Sons, Inc.

U2 - 10.1002/(SICI)1520-6610(1996)4:1<59::AID-JCD6>3.0.CO;2-Z

DO - 10.1002/(SICI)1520-6610(1996)4:1<59::AID-JCD6>3.0.CO;2-Z

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EP - 65

JO - Journal of Combinatorial Designs

JF - Journal of Combinatorial Designs

SN - 0364-9024

ER -

Hyperovals in the Known Projective Planes of Order 16

Abstract

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