Some new results of regular Hadamard matrices and SBIBD II

T. Xia, University of Wollongong
M. Xia, Central China Normal University, China
J. Seberry, University of Wollongong

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This article was originally published as: Xia, T, Xia, M & Seberry, J, Some new results of regular Hadamard matrices and SBIBD II, Australasian Journal of Combinatorics, 2007, 37, 117-125. The journal website is available here.

Abstract

In this paper we prove that there exist 4—{k2; ½k(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 q1, q2 and q3 are prime power such that q1 ≡ 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.