Existence conjecture for D-optimal difference families over abelian groups
Existence conjecture for D-optimal difference families over abelian groups
Let 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 is a pair of subsets of that group whose parameters are .
Existence conjecture. For each D-optimal parameter set there exists a difference family over some abelian group of order 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 and , were still unresolved; no resolution of the conjecture is supplied here.
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Sources & referencesView supporting material
Primary source
Dragomir Ž. Djoković, “A few new orders for D-optimal matrices”, arXiv:2210.03931 (2022).
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