Partitioning Steiner triple systems into complete arcs

For a Steiner triple system of order v to have a complete s-arc one must have s(s + 1)/2⩾v with equality only if s = 1 or 2 mod 4. To partition a Steiner triplesystem of order s(s + 1)2 into complete s-arcs, one must have s = 1 mod 4. In this paper wegive constructions of Steiner triple systems of order s(s + 1)2 which can be partitioned into complete s-arcs for all s = 1 mod 4. For s = 1 or 5 mod 12, we construct cyclic Steiner triple systems …