Breaking math records, one block at a time.
A covering design C(v,k,t) is the smallest set of k-number tickets drawn from 1…v such that every t-number combination appears on at least one ticket. The best known sizes are tracked in a public table of about 9,500 records. This page shows a MacBook taking the current record for each one, throwing a ticket away, and searching for a way to still cover everything. If it works, that's a new record: exactly one fewer.
Live
Records beaten
| Design | Old record | Ours | Status | File |
|---|---|---|---|---|
| None yet. The search is grinding — if one falls, it shows up here within seconds. | ||||
Running now
Each card is one CPU core. The big number is how many t-combinations are still uncovered with one ticket fewer than the record. It has to hit 0.
How it works, in miniature
C(7,3,2): tickets of 3 numbers from 1–7, and every pair must appear on some ticket. The record is 7 tickets, and that one's proven optimal. Click a ticket to throw it away and watch pairs go uncovered. The search on this page does the same thing on designs with tens of thousands of combinations, then reshuffles numbers on the remaining tickets until the red is gone.
Closest calls
| Design | Record | Uncovered at −1 | CPU time |
|---|---|---|---|
| Screening… | |||
Log
The fine print
What counts. A covering is easy to check and hard to find. Anyone can verify one by listing every t-combination and confirming it sits on a ticket. Every covering here is checked by an independent verifier before it's shown. A record becomes official only once the Covering Repository accepts it.
The search. Simulated annealing and weighted local search, written in C. Each run starts from the current record covering, drops the ticket that uniquely covers the least, and moves numbers between tickets to cover whatever is left uncovered. The targets are the roughly 2,600 open cells nobody has improved since April 2026.
Context. Since October 2026, people running AI-assisted searches have broken thousands of these records, so the easy ones are gone. This hunt goes after the cells the swarm hasn't touched.
Data. Record coverings come from Dan Gordon's La Jolla Covering Repository archive (Zenodo, April 2026). Current record sizes come from the Covering Repository table, checked 8 Nov 2026.