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Update 4a.md #90

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6 changes: 4 additions & 2 deletions constants/4a.md
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Expand Up @@ -19,8 +19,9 @@ Let $r(n)$ be the size of the largest cap set in $\mathbb{F}\_{3}^{n}$, i.e., a
| $2.1146$ | [P1970] |
| $2.2101$ | [CF1994] |
| $2.2173$ | [E2004] |
| $2.2180$ | [T2002] |
| $2.2180$ | [T2023] |
| $2.2202$ | [RBNBKDREWFKF2023] | Funsearch
| $2.2203$ | [ZWLPLZJZZZ2025] |X-evolve

## Additional comments and links

Expand All @@ -36,4 +37,5 @@ Let $r(n)$ be the size of the largest cap set in $\mathbb{F}\_{3}^{n}$, i.e., a
- [NS2016] Naslund, Eric; Sawin, William F. Upper bounds for sunflower-free sets. [arXiv:1606.09575](https://arxiv.org/abs/1606.09575)
- [P1970] Pellegrino, Giuseppe. Sul massimo ordine delle calotte in $S_{4,3}$. Matematiche (Catania) 25 (1970), no. 10, 1–9.
- [RBNBKDREWFKF2023] Romera-Paredes, Bernardino; Barekatain, Mohammadamin; Novikov, Alexander; Balog, Matej; Kumar, M. Pawan; Dupont, Emilien; Ruiz, Francisco J. R.; Ellenberg, Jordan S.; Wang, Pengming; Fawzi, Omar; Kohli, Pushmeet; Fawzi, Alhussein. Mathematical discoveries from program search with large language models. Nature. 625 (7995): 468–475 (2023).
- [T2002] Tyrrell, Fred. New lower bounds for cap sets. Discrete Analysis. 2023 (20). [arXiv:2209.10045](https://arxiv.org/abs/2209.10045).
-[ZWLPLZJZZZ2025] Zhai, Y., Wei, Z., Li, R., Pan, K., Liu, S., Zhang, L., Ji, J., Zhang, W., Zhang, Y. and Zhang, Y., 2025. \(X\)-evolve: Solution space evolution powered by large language models. arXiv preprint [arXiv:2508.07932].
- [T2023] Tyrrell, Fred. New lower bounds for cap sets. Discrete Analysis. 2023 (20). [arXiv:2209.10045](https://arxiv.org/abs/2209.10045).