Delandtsheer–Doyen parameters for block-transitive point-imprimitive 2-designs

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Abstract

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 m, n, now called Delandtsheer–Doyen parameters, linking the block size with the parameters of an associated imprimitivity system on points. We show that the Delandtsheer–Doyen 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–Doyen parameters.

Original languageEnglish
Article number9
Pages (from-to)2205-2221
Number of pages17
JournalDesigns, Codes, and Cryptography
Volume90
Issue number9
Early online date2 Mar 2022
DOIs
Publication statusPublished - Sept 2022

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