How many different (7,7,3,3,1) BIBD are there on vertex set[7]? 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?