Almost designs and their links with balanced incomplete block designs

  • Jerod MichelEmail author
  • Qi Wang


Almost designs (t-adesigns) were proposed and discussed by Ding as a certain generalization of combinatorial designs related to almost difference sets. Unlike t-designs, it is not clear whether t-adesigns need also be \((t-1)\)-designs or \((t-1)\)-adesigns. In this paper we discuss a particular class of 3-adesigns, i.e., 3-adesigns coming from certain strongly regular graphs and tournaments, and find that these are also 2-designs. We construct several classes of these, and discuss some of the restrictions on the parameters of such a class. We also construct several new classes of 2-adesigns, and discuss some of their properties as well.


Almost difference set Difference set Strongly regular graph t-adesign Tournament 

Mathematics Subject Classification

05B05 05E30 



The authors are very grateful to the three anonymous referees and to the Coordinating Editor for all of their detailed comments that greatly improved the quality and the presentation of this paper.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Computer Science and EngineeringSouthern University of Science and TechnologyShenzhenChina

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