Replacing large lookup table with switch statement
214 is 16384 entries. Each entry takes 2 bytes. That's 32768 bytes. That's all the flash the ATMega328P has.

The most efficient storage will be an array in flash, and that will take 100% of it. Using a switch will take more space.

So in short: no. Just no. It won't work whatever you try. You need to come up with a radically different storage solution (external flash memory?) or use a larger chip.  



As a side note, with "bit packing" you could reduce the storage to 20480 bytes, but doing a lookup of the data within that packed data (4 10-bit entries taking 5 bytes) will be slow to do since you have to work out exactly what combination of bits and bytes you need to reconstruct your 10-bit value.