Difference Systems of Sets (DSS)

A difference systems of sets (DSS) with parameters (n, τ₀, ..., τ_q-1,ρ) is a collection of q disjoint subsets Q_i of {1, 2, ..., n}, | Q_i| = τ_i, 0 ≤ i ≤ q-1, such that the multi-set

M={ a-b (mod n) | a ∈ Q_i, b ∈ Q_j , i≠j}

contains every number i (1 ≤ i ≤ n-1) at least ρ times. A DSS is perfect if every number i is contained exaclty ρ times in the multi-set of differences. A DSS is regular if all subsets Q_iare of the same size: τ₀ = τ₁ = ... = τ_q-1.

Here is some tables of different q :

Table 1: q = 2;

Table 2: q = 3;

Table 3: q = 4.