Abstract
A Steiner triple system can benested if it is possible to add one point to each block in such a way that a BIBD with block-size 4 and λ=1 is obtained. We prove that there exists a Steiner triple system of orderv that can be nested if and only ifvэ1 mod 6.
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References
Brouwer, A.E.: Optimal packings ofK 4's into aK n J. Comb. Theory (A)26, 278–297 (1979)
Colbourn, C.J., Colbourn, M.J.: Nested triple systems. Ars Comb.16, 27–34 (1983)
Lindner, C.C., Stinson, D.R.: The spectra for the conjugate invariant subgroups of perpendicular arrays. Ars Comb.18, 51–60 (1984)
Longyear, J.Q.: Nested transversals and small nested designs (preprint)
Mathon, R.A., Phelps, K.T., Rosa, A.: Small Steiner triple systems and their properties. Ars Comb.15, 3–110 (1983)
Mullin, R.C., Stinson, D.R., Vanstone, S.A.: Kirkman triple systems containing maximum subdesigns. Util. Math.21C, 283–300 (1982)
Wilson, R.M.: Constructions and uses of pairwise balanced designs. Math. Cent. Tracts55, 18–41 (1974)
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Stinson, D.R. The spectrum of nested Steiner triple systems. Graphs and Combinatorics 1, 189–191 (1985). https://doi.org/10.1007/BF02582943
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DOI: https://doi.org/10.1007/BF02582943