Cryptanalysis of Nonlinear Table Lookup
If the master key is strong (e.g. random 256-bit key), $c=1$ is fine, or you can use HKDF. A high number of iterations is only needed when you derive the key from a password or other low entropy string.
If you can store a 4000 element table securely, you could just use random keys instead of derived ones.
If you need the derived key to depend on a low entropy master key, you could use a randomly generated salt you keep secure. In that case leaking the salt will allow a brute force or dictionary attack on the master key, but without knowing the salt an attacker cannot attack it.


Optimally, your situation is 1. and you don't need to do anything special. 2. is also a secure alternative, but requires you to store more keys. You should only use 3. if you have no other options, and in that case you should use as high a $c$ as you can.



Now the actual question, is such a table secure?

If you have a large enough table that is only used for one key, it will not hurt the quality of the derived key. However, if that isn't the case, it may, since the keys will share the nonuniform probability distribution defined by the table.

An attacker who has the table could of course derive the key just as easily as when no table was used, so it is no better than using a random secret salt like I suggested in 3. above. So I wouldn't recommend using it.