A note on small defining sets for some SBIBD(4t-1, 2t-1, t-1)

We conjecture that p specified sets of p elements are enough to define an SBIBD(2p+ l,p,(p - 1)/2) when p ≡ 1(mod 4) is a prime or prime power. This means in these cases p rows are enough to uniquely define the Hadamard matrix of order 2p + 2. We show that the p specified sets can be used to first find the residual BIBD(p + 1,2p,p,(p + 1)/2,(p - 1)/2) for p prime or prime power. This can then be used to uniquely complete the SBIBD for p = 5,9,13 and 17. This is another case where a residual design with λ > 2 is completable to an SBIBD, the first such case having been given by Seberry in "On small defining sets for somee SBIBD(4t - 1, 2t - 1, t - 1)" . Bulletin ICA 4:58-62, 1992.