Developing an algorithm for triad design (Q712558)

This paper is along the theme of developing algorithmic methods to solve the difficult construction problems in block designs. To that end, a triad design \(TD(v)\) on \(v\) points is a peculiar way of listing the \(3\)-subsets of a \(v\)-set. A specific factor of the complete graph \(K_v\) is taken as a starter abd then developed to obtain a \(TD(v)\). The aim of the paper is an attempt to construct starters by considering the special cases \(v = 13\) and \(v = 19\) and the authors expect that this will help in solving the general case \(v \equiv 1 \pmod 6\).