How many different (7,7,3,3,1) BIBD are there on vertex set? Note that two such designs are different if their sets of blocks are different. That is, we do not require that the BIBDs be non-isomorphic; we simply require that they be non-identical.
I have found that we use construct the fano plane shape to illustrate this problem but counting part is difficult. I found the two ways to construct fano plane but any suggestion on how to count them up?