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Let $\mathcal{D}=\left(\mathcal{P},\mathcal{B} \right)$ be a symmetric$2$-$(v,k,\lambda )$ design admitting a flag-transitive, point-imprimitiveautomorphism group $G$ that leaves invariant a non-trivial partition $\Sigma$of $\mathcal{P}$. Praeger and Zhou \cite{PZ} have shown that, there is aconstant $k_{0}$ such that, for each $B \in \mathcal{B}$ and $\Delta \in\Sigma$, the size of $\left\vert B \cap \Delta \right \vert$ is either $0$ or$k_{0}$. In the present paper we show that, if $k>\lambda \left(\lambda-3\right)/2$ and $k_{0} \geq 3$, $\mathcal{D}$ is isomorphic to one of the knownflag-transitive, point-imprimitive symmetric $2$-designs with parameters$(45,12,3)$ or $(96,20,4)$.

Flag-transitive, point-imprimitive symmetric $2$-$(v,k,\lambda )$ designs with $k>\lambda \left(\lambda-3 \right)/2$