Year: 2026
Type: preprint
Abstract: The existence of sets of balanced incomplete block (BIB) designs with pairwise additivity, called pairwise additive BIB designs, has been studied through direct and recursive constructions in the literature. This paper presents a new method of constructing such designs from affine resolvable semi-regular group divisible (ARSRGD) designs. Since many known ARSRGD designs are obtained from generalized Hadamard matrices, we also describe the corresponding construction of pairwise additive BIB designs from generalized Hadamard matrices. Using the construction together with known existence results for generalized Hadamard matrices, we obtain several new infinite series of pairwise additive BIB designs, including designs with parameter sets whose existence was previously unknown.
Source: arXiv (Cornell University)
Authors: Matsubara, Kazuki, Kadowaki, Satoru
Language: English
Subfield: Discrete Mathematics and Combinatorics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7204113716