Cyclical Steiner triple systems orthogonal to their opposites (Q2277461)

A Steiner triple system (STS) consists of a set X together with a collection B of 3-subsets of X such that every pair of elements of X occurs in exactly one member of B. \((X,B_ 1)\) and \((X,B_ 2)\) are said to be orthogonal if \(B_ 1\cap B_ 2=\emptyset\) and for \((x,y,z)\in B_ 1\), \((u,v,z)\in B_ 1\) there exists no \(w\in X\) such that (x,y,w) and \((u,v,w)\in B_ 2.\) A cyclic STS(v) is a Steiner triple system on the set of residues mod v, having \((Z_ v,+)\) as its automorphism group. If \((Z_ v,B)\) is a cyclic STS(v), then multiplying by -1 will produce a cyclic STS(v) \((Z_ v,B')\) disjoint from \((Z_ v,B)\), i.e. \(B\cap B'=\emptyset\). The author gives a sufficient condition for \((Z_ v,B')\) to be orthogonal to \((Z_ v,B)\). An exhaustive search of cyclic STS(55) produced no solutions which satisfy this condition.