Three eggs, nine drops: tallest building

You hold $3$ identical eggs in a building with $n$ floors. There is an unknown critical floor $X$ with $1\le X\le n$: an egg dropped from below floor $X$ survives undamaged, and an egg dropped from floor $X$ or higher breaks. It is known that eggs break from the top floor $n$. What is the largest $n$ for which you can always determine $X$ using no more than $9$ drops?

130. With $e$ eggs and $d$ drops you can distinguish $\sum_{k=0}^{e}\binom{d}{k}$ possibilities: the first drop splits the problem into $(e-1,d-1)$ below and $(e,d-1)$ above. For $e=3,d=9$ this is $1+9+36+84=130$, so $X$ can be found among up to $130$ floors. Practically, first drop from floor $37$ (since two eggs and $8$ drops cover $36$ floors), then step up by $29, 22,\dots$