Large sets of extended directed triple systems with even orders (Q1045191)

Let \(X\) be a finite set of cardinality \(v\). An extended directed triple \((x,y,z)\) is a set of ordered pairs \((x,y)\), \((y,z)\), \((x,z)\) of not necessarily distinct elements of \(X\). An extended directed triple system \(EDTS(v)\) is a pair \((X,\mathcal A)\), where \(\mathcal A\) is a set of extended directed triples such that each ordered pair of elements belongs to exactly one extended triple. A large set \(LEDTS(v)\) of \(EDTS(v)\) is a collection \( \{(X,\mathcal A_k)\}_k\), where \(X\) is a \(v\)-set and each extended directed triple of \(X\) belongs to exactly one system \((X,\mathcal A_k)\). The authors prove that there exist \(LEDTS(v)\) for all even values, with the exception of \(v=4\).