An explicit family of 30 blocks meeting every 6-set of [60] in at least two points
Abstract
We exhibit an explicit family $\mathcal{B}$ of $30$ subsets (``blocks'') of size $6$ of $[60]=\{1,2,\dots,60\}$ with the following property: for every $6$-subset $S\subset[60]$, there exists a block $B\in\mathcal{B}$ such that $|S\cap B|\ge 2$. The construction is fully explicit and the proof is purely combinatorial.
Fields of Study & Subjects
Limits and Structures in Graph Theory
graph theory and CDMA systems
Computational Geometry and Mesh Generation
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 7 January 2026
- Document type
- Preprint