TITLE:
The Construction of Pairwise Additive Minimal BIB Designs with Asymptotic Results
AUTHORS:
Kazuki Matsubara, Sanpei Kageyama
KEYWORDS:
Incidence Matrix, Pairwise Balanced Design (PBD), Balanced Incomplete Block Design (BIBD), Additive BIB Design, Pairwise Additive BIB Design, Wilson’s Theorem
JOURNAL NAME:
Applied Mathematics,
Vol.5 No.14,
July
28,
2014
ABSTRACT: 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 = 2andλ = 1has 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, andalso for some land k the exact existence of lpairwise additive BIB designs
with block size k andλ = 1is discussed.