A partial Steiner ( n, k, l )‐system or briefly ( n, k, l )‐system is a pair ( V, S ), where V is an n ‐set and S is a collection of k ‐subsets of V , such that every l ‐subset of V is contained in at most one k ‐subset of S. A subset X ⊂ V is called independent if [ X ] k ∩ S = 0. The size of the largest independent set in S is denoted by α(S). Define The purpose of this note is to prove that for every k, l, k > l holds, where c, d are positive constants depending on k and l only.
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Rödl et al. (1994) studied this question.