Unitals in Projective Planes of Order 25
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Date
2023
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Basel Ag
Access Rights
info:eu-repo/semantics/closedAccess
Abstract
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.
Description
Keywords
Unital, Projective plane, Steiner design, Buekenhout-Metz Unitals, Designs
Journal or Series
Mathematics In Computer Science
WoS Q Value
N/A
Scopus Q Value
Q3
Volume
17
Issue
1
