PARTITIONING THE BLOCKS OF A STEINER TRIPLE SYSTEM INTO PARTIAL PARALLEL CLASSES

Does there exist a Steiner Triple System on v points, whose blocks can be partitioned into partial parallel classes of size m, where m ��� [v���3], m | b and b is the number of blocks of the STS(v)? We give the answer for 9 ��� v ��� 43. We also show that whenever 2|b, v ��� 3 (mod 6) we can find an STS(v) whose blocks can be partitioned into partial parallel classes of size 2, and whenever 4|b , v ��� 3 (mod 6), there exists an STS(v) whose blocks can be partitioned into partial parallel classes of size 4.