Covering designs
C(39,13,3,5) ≤ 12
The smallest known (39,13,3,5) covering uses 12 blocks, one fewer than the 13 known before. Quantavane published it on 26 October 2026.
Uploaded to coveringrepository.com on 26 October 2026 as Arhan Canli (Quantavane), where it became the listed record.
The record
| Ours | 12 blocks |
|---|---|
| Previous best | 13 blocks |
| Previous source | the value coveringrepository.com listed when we uploaded ours |
| Published | 26 October 2026 |
| Status | Uploaded to coveringrepository.com on 26 October 2026 as Arhan Canli (Quantavane), where it became the listed record. |
| Check | Checked exhaustively by three independent programs; verify.py in the public repository checks it again with plain Python. |
Every set of 5 of the 39 points shares at least 3 points with one of the 12 blocks of 13 points.
How it was found and checked
Found by a bit-parallel local search over (v,k,t,m) coverings. Checked exhaustively by three independent programs; verify.py in the public repository checks it again with plain Python.
git clone https://github.com/arhancanli/quantavane-covering-records
cd quantavane-covering-records
python3 verify.pyTake v points and blocks of k points each. A (v,k,t) covering design is a set of blocks such that every group of t points sits inside at least one block. C(v,k,t) is the fewest blocks that can do it. For most sizes no one knows the exact answer, so public tables keep the best covering anyone has found. Beating an entry means building a valid covering with fewer blocks.
Questions
What is C(39,13,3,5)?
The fewest blocks of 13 points, drawn from 39 points, such that every set of 5 points shares at least 3 points with some block.
Is 12 the smallest possible?
Not known; 12 is the smallest covering found so far.
What was the best known before?
13 blocks: the value coveringrepository.com listed when we uploaded ours.