%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 <em>k</em> = 2&nbsp;and&nbsp;<span style=\"font-size:9.0pt;font-family:&quot;\"><em>¦Ë</em> = 1&nbsp;</span>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&nbsp;also for some <em>l&nbsp;</em>and <em>k</em> the exact existence of <em>l</em>&nbsp;pairwise additive BIB designs
with block size <em>k</em> and&nbsp;<span style=\"font-size:9.0pt;font-family:&quot;\"><em>¦Ë</em> = 1&nbsp;</span>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