Generalised Bhaskar Rao designs of block size 3 over the group Z4

We show that the necessary conditions (i) 2tv(v-l) ≡ O(mod 3) (ii) v ≥ 3 (iii) t ≡ 1,5 (mod 6) => v ≠ 3 are sufficient for the existence of a GBRD(v,3,4t;Z4) except possibly when (v,t) = (27,1) or (39,1).