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

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 imprimi...

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Bibliographic Details
Published in:Designs, codes, and cryptography codes, and cryptography, 2022, Vol.90 (9), p.2205-2221
Main Authors: Amarra, Carmen, Devillers, Alice, Praeger, Cheryl E.
Format: Article
Language:English
Subjects:
Coding and Information Theory
Computer Science
Cryptology
Discrete Mathematics in Computer Science
Parameters
Permutations
Special Issue: The Art of Combinatorics – A Volume in Honour of Aart Blokhuis
Upper bounds
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Summary: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.
ISSN:0925-1022
1573-7586
DOI:10.1007/s10623-022-01015-5