Abstract
The following theorem is proved.
Theorem. An inequalityv ≧ (t + 1)(k −t + 1) + (k −t) holds for Steiner systemsS(t, k, v) witht < k < v andt even with equality if and only if (t, k, v) = (t, t + 1, 2t + 3) or (4, 7, 23).
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References
Cameron, P.J.: Parallelisms of Complete designs, London Math. Soc. Lecture Note 23. Cambridge Univ. Press, Cambridge. 1976
Hauck, P.: Eine Charakterisierung des SteinersystemsS(5, 8, 24). J. of Comb. theory Ser A32, 99–102 (1982)
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Noda, R. An inequality for steiner systems. Graphs and Combinatorics 7, 277–278 (1991). https://doi.org/10.1007/BF01787634
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DOI: https://doi.org/10.1007/BF01787634