Some new results of regular Hadamard matrices and SBIBD II

Authors

Tianbing Xia, University of WollongongFollow
Mingyuan Xia, Central China Normal UniversityFollow
Jennifer Seberry, University of WollongongFollow

RIS ID

19453

Publication Details

Xia, T., Xia, M. & Seberry, J. R. (2007). Some new results of regular Hadamard matrices and SBIBD II. Australasian Journal of Combinatorics, 37 117-126.

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 = 2^a3^bt², 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.