SBIBD(4k², 2k² + k, k² + k) and Hadamard matrices of order 4k² with maximal excess are equivalent

We show that an SBIBD(4k², 2k² + k, k² + k) is equivalent to a regular Hadamard matrix of order 4k² which is equivalent to an Hadamard matrix of order 4k² with maximal excess. We find many new SBIBD(4k², 2k² + k, k² + k) including those for even k when there is an Hadamard matrix of order 2k (in particular all 2k ≤ 210) and k є {1, 3, 5,...,29,33,...,41,45,51,53,61,...69,75,81,83,89,95,99,625,32m,25. 32m, m ≥ 0}.