Partitioning twofold triple systems into complete arcs (Q1198511)

Let \((V,B)\) be a block design. A set \(S \subset V\) is said to be an arc if \(| S \cap b | \leq 2\) for all blocks \(b \in B\). An arc \(S\) is said to be complete if \(S\) is maximal with respect to set inclusion. It is proved that for all \(s\), there exists a design with parameters \((s^ 2,3,2)\) such that the points can be partitioned into \(s\) complete \(s\)-arcs. Further, a general technique is presented which applies to the construction of \((s^ 2,4,1)\) designs having a partition into \(s\) complete \(s\)-arcs.