%0 Journal Article
%T The Construction of Pairwise Additive Minimal BIB Designs with Asymptotic Results
%A Kazuki Matsubara
%A Sanpei Kageyama
%J Applied Mathematics
%P 2130-2136
%@ 2152-7393
%D 2014
%I Scientific Research Publishing
%R 10.4236/am.2014.514207
%X An asymptotic existence of balanced incomplete block (BIB) designs and
pairwise balanced designs (PBD) has been discussed in [1]-[3]. On the other hand, the existence of additive BIB designs and pairwise
additive BIB designs with k = 2 and ¦Ë = 1 has been discussed with direct
and recursive constructions in [4]-[8]. In this paper, an asymptotic existence of pairwise additive BIB designs
is proved by use of Wilson¡¯s theorem on PBD, and also for some l and k the exact existence of l pairwise additive BIB designs
with block size k and ¦Ë = 1 is discussed.
%K Incidence Matrix
%K Pairwise Balanced Design (PBD)
%K Balanced Incomplete Block Design (BIBD)
%K Additive BIB Design
%K Pairwise Additive BIB Design
%K Wilson¡¯s Theorem
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=48161