Find a (16,6,1) Balanced incomplete block design (BIBD)

Question

I'm trying to find a balanced incomplete block design with the 16 items and $\lambda= 1$. I've calculated (using these defenitions) that a BIBD with 8 blocks and 6 items per block should be possible. However, when trying to contruct this with r, it only finds not-balanced sets.

A balanced set with $\lambda=2$ (and 16 blocks) can be found for example, but as the goal is to let participants rank sets of items, the target is to keep the effort to a minimum.

My question: is such a BIBD possible, and if yes, how do I construct a valid one?

Thanks in advance, Simon

Answer 1

For those interested, it's not possible. The first possibility with 16,6 is a lambda of 2.

Answer 2

Such a design cannot exist for it will violate Fisher's inequality.