For flag-transitive 4-designs with automorphism group PSL(2,q) and 5≤λ≤10, only eight design types exist, with two parameter sets left undecided; for λ>10 selected stabilizer types yield no designs.
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Flag-transitive $4$-designs and $PSL(2,q)$ groups
For flag-transitive 4-designs with automorphism group PSL(2,q) and 5≤λ≤10, only eight design types exist, with two parameter sets left undecided; for λ>10 selected stabilizer types yield no designs.