Some new results of regular Hadamard matrices and SBIBD II

In this paper we prove that there exist 4—{k2; 1/2k(k—1); k(k—2)} SDS, regular Hadamard matrices of order 4k2, and SBIBD(4k2, 2k2 + k, k2 + k) for k = 47, 71, 151, 167, 199, 263, 359, 439, 599, 631, 727, 919, 5q1, 5q2N, 7q3, where ql, q2 and q3 are prime power such that ql ≡ 1(mod 4), q2 ≡ 5(mod 8) and q3 ≡ 3(mod 8), N = 2a3bt2, a, b = 0 or 1, t ≠ 0 is an arbitrary integer. We find new SBIBD(4k2, 2k2 + k, k2 + k) for 43 values of k less than 1000. Publication Details This article was originally published as Xia, T, Xia, M and Seberry, J, Some new results of regular Hadamard matrices and SBIBD II, Australasian Journal of Combinatronics, December 2005. This journal article is available at Research Online: http://ro.uow.edu.au/infopapers/362