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A Method of Construction of Pairwise Additive Balanced Incomplete Block Designs

  • Kazuki Matsubara
  • Satoru Kadowaki
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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.

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Cite

BibTeXRIS
BibTeX
@misc{matsubara2026method,
  title = {{A Method of Construction of Pairwise Additive Balanced Incomplete Block Designs}},
  author = {Kazuki Matsubara and Satoru Kadowaki},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2608.21048},
  eprint = {2608.21048},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2608.21048},
}
RIS
TY  - UNPB
TI  - A Method of Construction of Pairwise Additive Balanced Incomplete Block Designs
AU  - Kazuki Matsubara
AU  - Satoru Kadowaki
PY  - 2026
DA  - 2026/10/23
PB  - arXiv
DO  - 10.48550/arxiv.2608.21048
UR  - https://arxiv.org/abs/2608.21048
AB  - 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.
ER  -