The Construction of Pairwise Additive Minimal BIB Designs with Asymptotic Results

• 作者: Kazuki Matsubara Sanpei Kageyama
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: Incidence Matrix Pairwise BALANCED DESIGN (PBD) BALANCED Incomplete Block DESIGN (BIBD) ADDITIVE BIB DESIGN Pairwise ADDITIVE BIB DESIGN Wilson’s Theorem
• 年，卷（期）: 2014,（14）
• 页码范围: 2130-2136
• 页数: 7页
• 分类号: O1

摘要

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.