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Codes Cryptogr."],"published-print":{"date-parts":[[2022,9]]},"abstract":"<jats:title>Abstract<\/jats:title><jats:p>Delandtsheer and Doyen bounded, in terms of the block size, the number of points of a point-imprimitive, block-transitive 2-design. To do this they introduced two integer parameters <jats:italic>m<\/jats:italic>,\u00a0<jats:italic>n<\/jats:italic>, now called Delandtsheer\u2013Doyen parameters, linking the block size with the parameters of an associated imprimitivity system on points. We show that the Delandtsheer\u2013Doyen parameters provide upper bounds on the permutation ranks of the groups induced on the imprimitivity system and on a class of the system. We explore extreme cases where these bounds are attained, give a new construction for a family of designs achieving these bounds, and pose several open questions concerning the Delandtsheer\u2013Doyen parameters.<\/jats:p>","DOI":"10.1007\/s10623-022-01015-5","type":"journal-article","created":{"date-parts":[[2022,3,3]],"date-time":"2022-03-03T11:07:26Z","timestamp":1646305646000},"page":"2205-2221","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":1,"title":["Delandtsheer\u2013Doyen parameters for block-transitive point-imprimitive 2-designs"],"prefix":"10.1007","volume":"90","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-4494-4359","authenticated-orcid":false,"given":"Carmen","family":"Amarra","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0766-4032","authenticated-orcid":false,"given":"Alice","family":"Devillers","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0881-7336","authenticated-orcid":false,"given":"Cheryl E.","family":"Praeger","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2022,3,3]]},"reference":[{"unstructured":"Alavi S.H., Daneshkhah A., Devillers A., Praeger C.E.: Block-transitive designs based on grids. arxiv:2201.01143.","key":"1015_CR1"},{"key":"1015_CR2","doi-asserted-by":"publisher","first-page":"430","DOI":"10.1016\/j.exmath.2019.04.005","volume":"38","author":"SL Aletheia-Zomlefer","year":"2020","unstructured":"Aletheia-Zomlefer S.L., Fukshansky L., Garcia S.R.: The Bateman-Horn conjecture: heuristics, history, and applications. 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