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

We shortly present two small results regarding the study formal duality in finite abelian groups as introduced by Cohn, Kumar, Reiher and Schürmann. In particular, 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 primitive formally dual sets of size $8$ in ${\mathbb{Z}}_8^2$.