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\(D\)-optimal exact designs in a completely randomized statistical set-up are constructed, for comparing \(n > 2\) qualitative factors (treatments), making \(r\) observations per treatment level in the presence of \(n\) (or less) quantitative or continuous factors (regression factors or covariates) of influence. Their relation with cyclic supplementary difference sets \(2-{(u; k_1, k_2; \lambda)}\) is shown, when \(n = 2u \equiv 2 \pmod{4}\), \(r \equiv 1 \pmod{2}\), \(r \neq 1\), \(r < u\) and \(k_1, k_2, \lambda\) are defined by \(1 \leq k_1 \leq k_2 \leq (u-1)/2\), \((u-2k_1)^2 + (u-2k_2)^2 = 2(ur+u-r)\), \(\lambda = k_1 + k_2 – (u-r)/2\). Making use of known cyclic difference sets, the existence of a multiplier and the non-periodic autocorrelation function of two sequences, such supplementary difference sets are constructed for the first time. A list of all 201 supplementary difference sets \(2-{(u; k_1, k_2; \lambda)}\) for \(n = 2u < 100\) is given.