Disjoint sets of distinct sum sets (Q1377746)

An \((h,J)\)-DS is a set \(A\) of \(J\) integers such that all sums of \(h\) elements of \(A\) (repetitions allowed) are distinct. An \((h,I,J)\)-DDS is a set \(\Delta= \{\Delta_1,\dots,\Delta_I\}\) of disjoint \((h,J)\)-DSs with positive elements. Let \(\nu(\Delta)\) be the maximum of the elements of the \(\Delta_i\). Several elementary constructions are given for such sets, mainly generalizing previous constructions for \(h=2\). If \(\nu(\Delta)=IJ\) the DDS is called perfect (this is the most interesting case): such a DDS exists (only) for \(I\) sufficiently large.