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PreprintCC BY 4.0arXiv

A tight single-change covering design with block size 6

  • Richard Bean
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Abstract

We give a tight single-change covering design with v=26 and k=6. This answers Problem 1 of the Nineteenth British Combinatorial Conference, which asked whether such a design exists with block size greater than $5$. We also describe the satisfiability search that found the design, including negative search results at the smallest admissible order v=21.

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Cite

BibTeXRIS
BibTeX
@misc{bean2026tight,
  title = {{A tight single-change covering design with block size 6}},
  author = {Richard Bean},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2607.10978},
  eprint = {2607.10978},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2607.10978},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - A tight single-change covering design with block size 6
AU  - Richard Bean
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2607.10978
UR  - https://arxiv.org/abs/2607.10978
AB  - We give a tight single-change covering design with v=26 and k=6. This answers Problem 1 of the Nineteenth British Combinatorial Conference, which asked whether such a design exists with block size greater than $5$. We also describe the satisfiability search that found the design, including negative search results at the smallest admissible order v=21.
ER  -