The minimum length of a base for the symmetric group acting on partitions

A base for a permutation group, GG, is a sequence of elements of its permutation domain whose stabiliser in GG is trivial. Using purely elementary and constructive methods, we obtain bounds on the minimum length of a base for the action of the symmetric group on partitions of a set into blocks of equal size. This upper bound is a constant when the size of each block is at most equal to the number of blocks and logarithmic in the size of a block otherwise. These bounds are asymptotically best possible.