A balanced incomplete block design (BIBD) is called a row-column directed BIBD (RCDBIBD) if:
1.
(i) it is directed in the usual sense, i.e., each ordered pair of points occurs an equal number of times in the blocks (directed column wise), and
2.
(ii) the blocks are arranged in such a way that (a) each point occurs an equal number of times in each row, and (b) each ordered pair of distinct points occurs an almost equal number of times in the rows.
The present paper gives construction techniques for RCDBIBDs and proves that the necessary conditions are sufficient for the existence of RCDBIBDs with block size 2. Existence of RCDBIBDs with block size 3 and v ≡ 1 mod 6 is shown and it is proved that an RCDBIBD(7,7,4,4,1∗) does not exist.
