In this paper we construct OD(4pq~r(q+1); pq~r, pq~r, pq~r, pq~r, pq~(r+1), pq~(r+1), pq~(r+1), pq~(r+1)) for each core order q ≡ 3(mod 4), r ≥ 0 or q = 1, p odd, p ≤ 21 and p ∈ {25, 49}, and COD(2q~r(q+1); q~r, q~r, q~(r+1), q~(r+1)) for any prime power q ≡ 1...