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The symmetric 2-(v,k,λ) designs with k>λ(λ−3)/2 admitting a flag-transitive point-imprimitive automorphism group are completely classified: they are the known 2-designs with parameters (16,6,2),(45,12,3),(15,8,4) or (96,20,4).
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Alessandro Montinaro (2024) studied this question.
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