Unital designs in planes of order 16
type: Item
instance of: scholarly article
title: Unital designs in planes of order 16
zbMATH Open document ID: 0940.05010
DOI: 10.1016/S0166-218X(99)00236-X
author: Stoicho D. Stoichev
author: Vladimir D. Tonchev
published in: Discrete Applied Mathematics
publication date: 2000-07-13T00:00:00Z
review text: A unital is any \(2\)-\((q^3 + 1, q + 1, 1)\) design. The classical example of a unital is an Hermitian curve embedded in \(\text{PG}(2, q^2)\). It should be noted that not all unitals of order \(q\) are embedded in projective planes of order \(q^2\). For the paper under review the authors search (non-exhaustively) for unitals embedded in the known planes of order 16. A total of 38 (inequivalent) unitals were found, and each of the known planes of order 16 contains at least one unital. The resulting 38 designs are mutually non-isomorphic as designs. Thus the total of known non-isomorphic \(2\)-\((65, 5, 1)\) designs is now 40, and 15 of these are resolvable.
Mathematics Subject Classification ID: 05B05
Mathematics Subject Classification ID: 51E20
zbMATH DE Number: 1436250
zbMATH Keywords: unital
zbMATH Keywords: projective planes of order 16
reviewed by: Gary L. Ebert
MaRDI profile type: Publication
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full work available at URL: s0166-218x(99)00236-x
OpenAlex ID: W1970755458
Wikidata QID: Q128017868
description: scientific article; zbMATH DE number 1436250