**MSC:**- 05B05 Block designs, See also {51E05, 62K10}

(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.