Some new results of regular Hadamard matrices and SBIBD II

Authors

Tianbing Xia, University of WollongongFollow
M. Xia, Central China Normal University, ChinaFollow
Jennifer Seberry, University of WollongongFollow

RIS ID

19453

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 Combinatorics, 37 117-126, 2007.

Abstract

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.