Regular Hadamard Matrices, Maximum Excess and SBIBD

When k = q1, q2, q1q2, q1q4, q2q3N, q3q4N, q1, q2 and q3 are prime power, where q1 ≡ 1 (mod 4), q2 ≡ 3 (mod 8), q3 ≡ 5 (mod 8), q4 = 7 or 23, N = 2a3bt2, a, b = 0 or 1, t ≠ 0 is an arbitrary integer, we prove that there exist regular Hadamard matrices of order 4k2, and also there exist SBIBD(4k2, 2k2 + k, k2 + k). We find new SBIBD(4k2, 2k2 + k, k2 + k) for 233 values of k.