Every record packing for n ≤ 324 was found by someone, usually by building on someone else's. This page credits them: who holds each record now, who held it before, how long each record stood, and who proved the floors underneath. Some records from 1979 still stand; others have changed hands three times this autumn.
Every record, by age
Darker means the current record is older. Outlined cells are the plain grid packing (side ⌈√n⌉), which no one has beaten, or for perfect squares can't. Click a cell for its full history below.
Click a column to sort, a name to see their n and outline them on the map. Records: n where they found the current record; ever: where they held it at some point; record-years: how long their records stood, added up (split between co-finders); built on: current records constructed from their packings by others or by the catalogue (Göbel's "L" additions, mostly); floors: n where they proved the best lower bound now known, and ever.
who
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Longest-standing records
Open n whose record is oldest: beat one of these and you have beaten a classic.
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Newest records
The latest records, with the packing each one built on where its finder said so.
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How credit is counted
Records change hands when someone finds or improves the best packing. Refining an existing packing (re-optimizing it, fixing it, computing its side exactly) is credited on that n but leaves the record with its finder.
Constructions. Many records extend a smaller one, usually by adding "L"-shaped strips to a packing of Frits Göbel's from 1979. Where the catalogue names no finder for the extension, the record is shown as built on the original packing and counted in its author's built on column, not as a find.
Lineage since September 2026. When a later packing starts from someone else's, we ask whether the two are the same local minimum: can one be moved continuously into the other without the side ever exceeding the larger of the two? If a computer check certifies such a path, the later posting is a refinement and the record stays with the original finder. If not, the later poster found a new packing: it is credited to them, "based on" the earlier one. Until a case is decided, two postings within 10−7 of each other count as one packing, credited to the earlier.
Floors count the lower bounds the Bounds page uses: published proofs and the 2026 computer-checked certificates (unrefereed). Nagamochi's 2005 theorem, whose published proof has a gap, and floors reported without a certificate are listed but not counted. So, for now, is our own s(k² − 4) = k family, until jlevy/squares has replayed it. When two floors are equal, the earlier one holds.
Sources. Credits up to mid-September 2026 are read from David Ellsworth's catalogue (which carries Erich Friedman's earlier history); later ones from the posts themselves, mostly on jlevy/squares. "First" is as best we know it. If you see a credit that's wrong or missing, please open an issue.
Want to get on the board? The open n above are all fair game; new records are registered at jlevy/squares, and this page picks them up from there.