Results
First verified records.
Ten covering designs, each using one block fewer than the best known before. Our search engine found them on a laptop, at no cost, and every one was checked exhaustively.
Submitted to coveringrepository.com on 22 October 2026. Awaiting the table's acceptance.
What a covering design is
Take 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.
The ten entries
| Entry | Our blocks | Previous best | Check |
|---|---|---|---|
| C(65,14,2) | 28 | 29 | every pair covered |
| C(66,12,2) | 38 | 39 | every pair covered |
| C(70,21,2) | 15 | 16 | every pair covered |
| C(71,16,2) | 26 | 27 | every pair covered |
| C(75,17,2) | 26 | 27 | every pair covered |
| C(76,14,2) | 38 | 39 | every pair covered |
| C(94,17,2) | 39 | 40 | every pair covered |
| C(42,12,3) | 76 | 77 | every triple covered |
| C(47,21,3) | 21 | 22 | every triple covered |
| C(49,13,3) | 81 | 82 | every triple covered |
Previous best: the La Jolla Covering Repository's final data (Daniel M. Gordon, CC BY 4.0), still the listed value on coveringrepository.com when we checked on 22 October 2026.
Check them yourself
The coverings and a short checker are public. The checker uses plain Python and tests every group of points, so you don't have to trust us.
git clone https://github.com/arhancanli/quantavane-covering-records
cd quantavane-covering-records
python3 verify.pyThe engine that found them is open source: github.com/arhancanli/quantavane.
What runs next
The engine now works through thousands of open entries around the clock, in covering designs and the wider family of lottery coverings. Every new result goes through the same two checks before it appears here.
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