Existence status of some previously open abelian difference sets

We theoretically establish the existence status of some previously open abelian difference sets. More precisely, we show the nonexistence of all the following difference sets: (841,120,17)(841,120,17) in Z29×Z29Z29×Z29, (364,121,40)(364,121,40) in Z2×Z2×Z7×Z13Z2×Z2×Z7×Z13, (837,133,21)(837,133,21) in Z3×Z3×Z3×Z31,Z3×Z9×Z31Z3×Z3×Z3×Z31,Z3×Z9×Z31 and Z837Z837.