Eight octads suffice
Let \(\Omega\) be a Steiner system S(5,8,24). It is shown that there exists a set of eight blocks, or octads, in \(\Omega\) such that \(\Omega\) is the only such Steiner system that contains all eight of them. Thus this set of eight octads determines \(\Omega\). No set of seven octads has this property.
scientific article; zbMATH DE number 3841887