On the 3BD-closed set \(B_3(\{4,5\})\) (Q1886341)

For each \(v\not= 13\) fulfilling the existence condition \(v\equiv 1,2,4,5,8,10\pmod{12}\) there exists a \(3\)-design of \(v\) points with block sizes belonging to \(\{4,5\}\). Proofs are obtained by recursive constructions using many little tables of suitable incidence structures and by previous results obtained e.g. by Hanani and by the author.