Unitals in the Desarguesian projective plane of order 16

John Bamberg; A. Betten; Cheryl Praeger; A. Wassermann

doi:10.1016/j.jspi.2012.10.006

Unitals in the Desarguesian projective plane of order 16

John Bamberg, A. Betten, Cheryl Praeger, A. Wassermann

Research output: Contribution to journal › Article

8 Citations (Scopus)

Abstract

Using computer, we classify the unitals in the Desarguesian projective plane of order 16. We use computational methods based on analysis involving tactical decompositions to break symmetry, making a computer search feasible. We prove that all unitals in PG(2, 16) are known, namely, up to isomorphism, there are exactly two Buekenhout-Metz unitals (one of them the Hermitian curve). © 2012 Elsevier B.V.

Original language	English
Pages (from-to)	110-122
Journal	Journal of Statistical Planning and Inference
Volume	144
Issue number	1
DOIs	https://doi.org/10.1016/j.jspi.2012.10.006
Publication status	Published - 2014

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abstract = "Using computer, we classify the unitals in the Desarguesian projective plane of order 16. We use computational methods based on analysis involving tactical decompositions to break symmetry, making a computer search feasible. We prove that all unitals in PG(2, 16) are known, namely, up to isomorphism, there are exactly two Buekenhout-Metz unitals (one of them the Hermitian curve). {\textcopyright} 2012 Elsevier B.V.",

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AU - Betten, A.

AU - Praeger, Cheryl

AU - Wassermann, A.

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AB - Using computer, we classify the unitals in the Desarguesian projective plane of order 16. We use computational methods based on analysis involving tactical decompositions to break symmetry, making a computer search feasible. We prove that all unitals in PG(2, 16) are known, namely, up to isomorphism, there are exactly two Buekenhout-Metz unitals (one of them the Hermitian curve). © 2012 Elsevier B.V.

U2 - 10.1016/j.jspi.2012.10.006

DO - 10.1016/j.jspi.2012.10.006

M3 - Article

VL - 144

SP - 110

EP - 122

JO - Journal of Statistical Planning and Inference

JF - Journal of Statistical Planning and Inference

SN - 0378-3758

IS - 1

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