Abstract
In this paper we prove that there exist 4-{ v; k, k, k, k; λ} supplementary difference sets (SDSs) with v = q 2, q ≡ 1 (mod 4) a prime power, k = q(q − 1) 2 , λ = 4 k − v, and Williamson matrices of order 4 tv for t ϵ S = {2 k + 1:0 ⩽ k ⩽ 16} ∪ {37, 59, 61, 67 } ∪ {2 i · 10 j · 26 k +1: i, j, k ⩾0}.
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