New construction of disjoint distinct difference sets (Q1273535)

An \((I,J)\)-DDDS is a set \(\Delta =\{\Delta_i\}_{i\in I}\) where \(\Delta_i=\{a_{ij}\}_{j\in J}\) (\(a_{ij}\) positive integers) such that for each \(i\) all the differences \(a_{ij}-a_{ij'}\) with \(j\not = j'\) are distinct. If \(\max\{a_{ij}\}=IJ\) then the \((I,J)\)-DDDS is called regular. It is called multiplicative if there exists integers \(v,f_1=1,f_2,\dots,f_I\) such that \(\Delta_i\{f_ia\}_{a\in \Delta_1}\pmod v\). It is called additive if there is a sequence \(\{a_i\}_{i\in J}\) such that \(a_{ij}=a_j+i\pmod I\) and \((j-1)I<a_{ij}\leq jI\). Elementar constructions and examples of the above-mentioned structures are also given using classical difference families. Several theoretical and techincal applications are quoted.