diff --git a/constants/24a.md b/constants/24a.md index 1e8d3cd..c0bcf1e 100644 --- a/constants/24a.md +++ b/constants/24a.md @@ -31,7 +31,7 @@ Since it is not known whether $C_{24}$ is finite, results are typically stated a | Bound | Reference | Comments | | ----- | --------- | -------- | -| $n$ | Trivial | Since $\|\|A_{\ast j}\|\|_{2}\le 1$ implies $\lvert a_{ij}\rvert\le 1$, we have $\|\|Ax\|\|_{\infty}\le n$ for every $x\in\{-1,1\}^{n}$. | +| $n$ | Trivial | Since $\|\|A\_{\ast j}\|\|\_{2}\le 1$ implies $\lvert a_{ij}\rvert\le 1$, we have $\|\|Ax\|\|_{\infty}\le n$ for every $x\in\{-1,1\}^{n}$. | | $O(\log n)$ | [Bec1981], [Spe1985], [Glu1989] | Partial-coloring/entropy-method bounds yield $O(\log n)$ discrepancy for Komlós-type instances. | | $O(\sqrt{\log n})$ | [Ban1998] | Banaszczyk’s vector-balancing theorem (via Gaussian measure) gives the first $o(\log n)$ bound. | | $O(\sqrt{\log n})$ (poly-time) | [BDG2019] | Polynomial-time algorithm matching Banaszczyk’s existential bound up to constants. | @@ -72,4 +72,4 @@ Since it is not known whether $C_{24}$ is finite, results are typically stated a # Acknowledgements -Prepared with assistance from ChatGPT 5.2 Pro. \ No newline at end of file +Prepared with assistance from ChatGPT 5.2 Pro.