(261, 105, 42) Abelian Difference Sets Do Not Exist

Difference sets in the group Z3 x Z3 x Z37 and the group Z3 x Z9 x Z7 are known not to exist. The only open abelian case with a sylow-3 subgroup rank 2 listed in Vera-Lopez and Sanchez\u27s table is Z3 x Z3 x Z29. We prove for Vera-Lopez and Sanchez\u27s table that difference sets do not exist in the open group allowing the appropriate entry to be no . We also prove that there exist no difference sets (261, 105, 42) for any group with order 261