A method for finding initial difference blocks for certain balanced incomplete block designs by means of partitions of elements in finite rings is given. It is shown that multiplier theory for difference sets, when expressed. It terms of finite rings, can be useful in certain instances for obtaining appropriate partitions. In particular, despite the non-existence of a difference set for a (49, 49, 16, 16, 5) design, one can construct a (49, 98, 32, 16, 10) design by attempting the former.