*PN* 96/2 TI eng: On the Number of Indecomposable Block Designs dt: \"Uber die Anzahl elementarer Block-Designs AU Gr\"uttm\"uller, Martin SO Preprint 96/2, ISSN 0948-1028 LA englisch AB A $t$-$(v,k,\lambda)$ design $\mathcal{D}$ is a system (multiset) of $k$-element subsets (called blocks) of a $v$-element set $V$ such that every $t$-element subsset of $V$ occurs exactly ${\lambda}$ times in the blocks of $\mathcal{D}$. A $t$-$(v,k,\lambda)$ design $\mathcal{D}$ is called indecomposable (or elementary) if and only if there is no subsystem which is a $t$-$(v,k,\lambda ')$ design with $0<\lambda '<\lambda$. It is known that the number of indecomposable designs for given parameters $t,v,k$ is finite. A block design is a is $t$-$(v,k,\lambda)$ design with $t=2$. The exact number of non-isomorphic, indecomposable block designs is only known for $k=3$ and $v\le 7$. We computed the number of indecomposable designs for $v\le 13$ and $\lambda\le 6$. The algorithms used will be described. CC 05B05 UT design, indecomposable