Even if we conservatively assume that you only need lowercase characters, and that you need one bit per password, that's still 26^16 bits = 4.6 ZB, about fifteen times the total capacity of every hard disk sold by Seagate in 2011 (330 EB).
People here don't know what rainbow tables are. If you asked them to build a rainbow table, you'd get... a table. (You're right.)
Thank you for the contentless comment. Instead, you might consider offering a more interesting algorithm, its tradeoffs, and why it is beneficial to take more computation time?
A rainbow table doesn't store every hash for the password space it's built for. I'm sure you already knew that, but decided to pretend otherwise when calculating the size of one.