On flag-transitive imprimitive 2-designs

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In 1987, Huw Davies proved that, for a flag-transitive point-imprimitive 2- (Formula presented.) design, both the block-size (Formula presented.) and the number (Formula presented.) of points are bounded by functions of (Formula presented.), but he did not make these bounds explicit. In this paper we derive explicit polynomial functions of (Formula presented.) bounding (Formula presented.) and (Formula presented.). For (Formula presented.) we obtain a list of “numerically feasible” parameter sets (Formula presented.) together with the number of parts and part-size of an invariant point-partition and the size of a nontrivial block-part intersection. Moreover from these parameter sets we determine all examples with fewer than 100 points. There are exactly 11 such examples, and for one of these designs, a flag-regular, point-imprimitive (Formula presented.) design with automorphism group (Formula presented.), there seems to be no construction previously available in the literature.

Original languageEnglish
Pages (from-to)552-574
Number of pages23
JournalJournal of Combinatorial Designs
Issue number8
Publication statusPublished - Jul 2021


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