In this talk, we consider problems and results that go in the opposite direction of the classical theorems in the discrepancy theory. The following statement gives a flavor of our approach. Let t, k and q be integers such that q≥0, 0≤t<k, and t≡k(mod2), and take s∈[0,t+1] as the unique integer satisfying s≡q+k−t−22(mod(t+2)).