Stoichev, Stoicho D. D.Gezek, Mustafa2023-05-062023-05-0620231661-82701661-8289https://doi.org/10.1007/s11786-023-00556-9https://hdl.handle.net/20.500.11776/11974In 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.en10.1007/s11786-023-00556-9info:eu-repo/semantics/closedAccessUnitalProjective planeSteiner designBuekenhout-Metz UnitalsDesignsArticle171N/AWOS:0009490296000012-s2.0-85150179370Q3