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We shortly present two small results regarding the study formal duality infinite abelian groups as introduced by Cohn, Kumar, Reiher and Sch\"urmann. Inparticular, we give a new example of a formally self dual set in$\mathbb{Z}_2^2\times\mathbb{Z}_4^2$ and computed nonexistence of primitiveformally dual sets of size $8$ in $\mathbb{Z}_8^2$.

Results on formally dual sets in finite abelian groups of size 64 obtained from a graph search algorithm