Author(s)

Kazuki Matsubara, Sanpei Kageyama

Graduate School of Science, Hiroshima University, Higashi-Hiroshima, Japan.
Hiroshima Institute of Technology, Hiroshima, Japan.

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 λ = 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 λ = 1 is discussed.

Incidence Matrix, Pairwise Balanced Design (PBD), Balanced Incomplete Block Design (BIBD), Additive BIB Design, Pairwise Additive BIB Design, Wilson’s Theorem

Matsubara, K. and Kageyama, S. (2014) The Construction of Pairwise Additive Minimal BIB Designs with Asymptotic Results. Applied Mathematics, 5, 2130-2136. doi: 10.4236/am.2014.514207.