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Give an example of BIBD(balanced Incomplete Block Design) with no repeated blocks in which λ > k.

Here which I need to find a BIBD where λ(each pair of vertices occurs together in exactly λ blocks) is greater than k(each block contains k vertices). For example, (v,b,r,1,2).

any suggestions?

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    Sorry, comment above was nonsense. But $\lambda=2$, $k=1$ can't possibly work - how can a pair of vertices appear in any blocks at all if each block has only one vertex? $\lambda=3$, $k=2$ can only be achieved if you allow multiple copies of some blocks. So I think you have to go to $\lambda=4$, $k=3$ to get any useful solution. See my answer.2012-04-19

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Take a set of size 6, and let the blocks be the subsets of size 3. I think you'll find this works with $\lambda=4$, $k=3$.

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    $b$ is the number of blocks, which is the number of 3-subsets of a 6-set, which is *not* 40. $r$ is the number of 3-element subsets of abcdef containing f.2012-04-19