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Supplementary difference sets and optimal designs. (English) Zbl 0756.05032
Summary: \(D\)-optimal designs of order \(n=2v\equiv 2\pmod 4\), where \(q\) is a prime power and \(v=q^ 2+q+1\) are constructed using two methods, one with supplementary difference sets and the other using projective planes more directly. An infinite family of Hadamard matrices of order \(n=4v\) with maximum excess \(\sigma(n)=n\sqrt{n-3}\) where \(q\) is a prime power and \(v=q^ 2+q+1\) is a prime, is also constructed.

MSC:
05B10 Combinatorial aspects of difference sets (number-theoretic, group-theoretic, etc.)
05B20 Combinatorial aspects of matrices (incidence, Hadamard, etc.)
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