Journal of Statistical Theory and Practice

, Volume 7, Issue 4, pp 783–790 | Cite as

The Existence of Two Pairwise Additive BIBD(v, 2, 1) for Any v

  • K. Matsubara
  • S. KageyamaEmail author


The existence of additive balanced incomplete block (BIB) designs has been discussed with direct and recursive constructions in Sawa et al. (2006). In this article, pairwise additive BIB designs are proposed and then new recursive methods of constructing such designs are provided. It is finally shown that for any integer v, two pairwise additive B(v, 2, 1) can be constructed. As a by-product we present a recursive construction of multiply nested BIB designs of block sizes 2 for some .


Incidence matrix Balanced incomplete block (BIB) design Additive BIB design Pairwise additive BIB design Nested BIB design Multiply nested BIB design Ordered design Perpendicular array 


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Copyright information

© Grace Scientific Publishing 2013

Authors and Affiliations

  1. 1.Graduate School of ScienceHiroshima UniversityHigashi-HiroshimaJapan
  2. 2.Hiroshima Institute of TechnologyHiroshimaJapan

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