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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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