On set systems not containing delta systems (Q1187943)

Denote \(\varphi(n,k)\) the least integer such that every \(n\)-uniform hypergraph having at least \(\varphi(n,k)\) edges contains an \(k\)-element (strong) delta system. (The existence of such a function is guaranteed by the well-known Erdős-Rado theorem [J. Lond. Math. Soc. 35, 85--90 (1960; Zbl 0103.27901)].) This paper contains some concrete constructions (for small pairs of \((n,k))\) improving the lower bound for \(\varphi(n,k)\), as well as the analogue lower bound for weak delta systems. The constructions were produced by both analytical and computational methods.