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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?

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    I don't understand this question. You have a unique such object upto isomorphism---Fano plane. Are you looking for the number of ways to renumber the 7 points on the Fano Plane?2012-04-19
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    @Kannappan, I understand the problem to be, given a 7-set, how many different Fano planes are there, if Fano planes are different when they don't have the same 7 3-sets. See my answer.2012-04-19

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