Designs, Codes and Cryptography

, Volume 87, Issue 7, pp 1521–1540 | Cite as

On existence theorems for simple t-designs

  • Tran van TrungEmail author


The paper concerns a study of our previous general construction for simple t-designs, called the basic construction, with the goal to establish existence theorems for t-designs. As a general framework the basic construction involves a great deal of possibilities of combining ingredient designs, and thus computations are necessary for constructing designs by this method. The work shows the results of an investigation finding specified conditions under which the required computations can be avoidable. They thus lead to existence theorems for simple t-designs and many of them have been found. Also a large number of examples are included to illustrate the results.


Simple t-design Existence theorem Recursive construction 

Mathematics Subject Classification




  1. 1.
    Beth T., Jungnickel D., Lenz H.: Design Theory, 2nd edn. Cambridge Univ. Press, Cambridge (1999).CrossRefzbMATHGoogle Scholar
  2. 2.
    Colbourn C.J., Dinitz J.H. (eds.): Handbook of Combinatorial Designs, 2nd edn. CRC Press, Boca Raton (2007).zbMATHGoogle Scholar
  3. 3.
    Stinson D.R.: Combinatorial Designs: Constructions and Analysis. Springer, New York (2003).zbMATHGoogle Scholar
  4. 4.
    van Trung T.: On the construction of \(t\)-designs and the existence of some new infinite families of simple \(5\)-designs. Arch. Math. 47, 187–192 (1986).MathSciNetCrossRefzbMATHGoogle Scholar
  5. 5.
    van Trung T.: Simple \(t\)-designs: a recursive construction for arbitrary \(t\). Des. Codes Cryptogr. 83, 493–502 (2017). Scholar
  6. 6.
    van Trung T.: A recursive construction for simple \(t\)-designs using resolutions. Des. Codes Cryptogr. 86, 1185–1200 (2018). Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Institut für Experimentelle MathematikUniversität Duisburg-EssenEssenGermany

Personalised recommendations