Design

Definition

A $t$-$(v,k,\lambda )$ design is a point-block geometry $(\mathcal{P},\mathcal{B})$ where $\mathcal{P}$ is a set of $v$ points and $\mathcal{B}$ is a collection of $k$-subsets of $\mathcal{P}$, with the property that every $t$-subset of $\mathcal{P}$ is contained in exactly $\lambda$ blocks of $\mathcal{B}$.

We say a design is a symmetric design if $t=2$ and $v=|\mathcal{B}|$.

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ref: A classification of finite partial linear spaces with a primitive rank 3 automorphism group of almost simple type