A curated collection of optimization constants
- Here is an initial blog post introducing the project: A crowdsourced repository for optimization constants?, 22 Terence Tao, January 2026.
We are arbitrarily numbering the constants as
| Number | Description | Best lower bound | Best upper bound |
|---|---|---|---|
| 1 | Sidon set autocorrelation constant | 1.2802 | 1.5029 |
| 2 | Erdős minimum overlap constant | 0.379005 | 0.380876 |
| 3 | Gyamarti-Hennecart-Ruzsa sum-difference constant | 1.173077 | 1.33333 |
| 4 | Cap set constant | 0.724851 | 0.782597 |
| 5 | A Sidon set constant | 0 | 0.97633 |
| 6 | Union-closed sets conjecture constant | 0.38271 | 0.5 |
| 7 | The irrationality measure of |
2 | 7.103205334137 |
| 8 | Classical zero-free region constant | 0.755106 | 5.558691 |
| 9 | Shannon capacity of the 7-cycle | 3.2578 | 3.3177 |
| 10 | The real Grothendieck constant | 1.67696 | 1.782214 |
| 11 | The |
||
| 12 | The Beardwood–Halton–Hammersley constant | 0.6277 | 0.90304 |
| 13 | The arithmetic sums-differences constant | >1.77898 | 1.83333 |
| 14 | Smallest |
6 | 432 |
| 15 | Matrix multiplication exponent | 2 | < 2.3728596 |
| 16 | Brezis–Gallouet–Wainger remainder constant on the 2D torus | ||
| 17 | Exponential growth constant of diagonal Ramsey numbers | 3.7992027396 | |
| 18 | Marton's conjecture constant (PFR) | 1 | 9 |
| 19 | The critical exponent for isoperimetric inequality on the hamming cube | 0.5 | 0.50057 |
| 20 | The Crouzeix constant | 2 | 11.08 |
| 21 | The Berry–Esseen constant | 0.4097321837 | 0.4690 |
This site is maintained by Damek Davis, Paata Ivanisvili and Terence Tao.
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