Journal of Applied Mathematics and Computing

, Volume 40, Issue 1–2, pp 195–207 | Cite as

Remarks on the concepts of t-designs

  • Eiichi Bannai
  • Etsuko Bannai
Discrete and combinatorial mathematic


We define the concept of t-design for real hyperbolic space ℍ n , as an analogue of the definition of Euclidean t-design. Then, we discuss the similarities between the concept of t-design on ℍ n or ℝ n , and the concept of relative t-design defined for association schemes by Delsarte: Pairs of vectors in the space of an association scheme (1977).


Real hyperbolic space t-design Spherical design Euclidean design Relative t-design 

Mathematics Subject Classification (2010)

05E99 05E30 05B99 51M04 51M09 



This work was done while the authors are visiting Hebei Normal University for 3 months, from Sept. to Dec. 2010. The authors thank Professor Suogang Gao and Hebei Normal University for their hospitalities. The authors thank the referees for valuable comments.


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Copyright information

© Korean Society for Computational and Applied Mathematics 2012

Authors and Affiliations

  1. 1.Department of MathematicsShanghai Jiao Tong UniversityShanghaiChina
  2. 2.Itoshimashi, FukuokaJapan

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