This proof demonstrates the existence of (n,q,2)-Steiner systems in hypergraphs under specific conditions, indicating its significance in combinatorial design.
We prove that if p greater than or equals n Superscript minus left parenthesis q minus 6 right parenthesis divided by 2 p ≥ n − ( q − 6 ) / 2 p ≥ n-(q-6)/2 , then asymptotically almost surely the binomial random q -uniform hypergraph script upper G Superscript left parenthesis q right parenthesis Baseline left parenthesis n comma p right parenthesis G ( q ) ( n , p ) G(q)(n,p) contains an ( n , q , 2)-Steiner system, provided n satisfies the necessary divisibility conditions.
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Delcourt et al. (2026) studied this question.
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