Existence conjecture for D-optimal difference families over abelian groups

Let $(v;r,s;\lambda)$ be a D-optimal parameter set, meaning that it is the parameter set of a D-optimal difference family and satisfies the D-optimality conditions. A difference family over a group of order $v$ is a pair of subsets of that group whose parameters are $(v;r,s;\lambda)$.

Existence conjecture. For each D-optimal parameter set $(v;r,s;\lambda)$ there exists a difference family over some abelian group of order $v$ having these parameters.

D-optimal difference families yield D-optimal matrices, so the conjecture would establish existence of a suitable matrix for every D-optimal parameter set. The source notes that some parameter sets, including $(85;39,34;31)$ and $(99;43,42;36)$, were still unresolved; no resolution of the conjecture is supplied here.