A tight single-change covering design with block size 6

Richard Bean

A tight single-change covering design with block size 6

Combinatorics 2026-07-13 v1 Discrete Mathematics

Authors: Richard Bean

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 $v=21$ .

Keywords

covering design single-change block size combinatorial design satisfiability search existence

Cite

@article{arxiv.2607.10978,
  title  = {A tight single-change covering design with block size 6},
  author = {Richard Bean},
  journal= {arXiv preprint arXiv:2607.10978},
  year   = {2026}
}

Comments

9 pages