Unitals in Projective Planes of Order 25

Unitals in Projective Planes of Order 25

In this paper, results of a non-exhaustive computer search for unitals in the known planes of order twenty-five are reported. The 2-(126, 6, 1) designs associated with newly found unitals are studied in detail. 938 non-isomorphic unital designs are discovered and we show that three of the unital des...

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Veröffentlicht in:Mathematics in computer science 2023-03, Vol.17 (1), Article 5
Hauptverfasser: Stoichev, Stoicho D., Gezek, Mustafa
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ACA 2021
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description In this paper, results of a non-exhaustive computer search for unitals in the known planes of order twenty-five are reported. The 2-(126, 6, 1) designs associated with newly found unitals are studied in detail. 938 non-isomorphic unital designs are discovered and we show that three of the unital designs are embeddable in two non-isomorphic planes and 239 of them are resolvable. The findings of this study improve some well-known lower bounds on the number of such designs and provide new connections between some pairs of planes. A conjecture concerning the p -ranks of unital designs embedded in planes of order q 2 is formulated.
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Computer Science
Lower bounds
Mathematics
Mathematics and Statistics
title Unitals in Projective Planes of Order 25
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