According to a source-book I have, '81s with a stick came with 2.72:1 gears; autos came with 2.87:1 gears.
Your car came with a Dana-44-type housing, and as stated earlier, you can run ratios up-to 3.73 (numerically) with the original carrier.
In August, I bought 3.73s gears, new and in-the-box, for $125 + S&H, from a place on Long Island ( "POWER TRAIN". I spoke to 'Ronnie" @ 1-631-589-7020. These ARE brand-new, in-the-box, and they DO fit '80-'82 Corvettes. "Ronnie" seems very nice and informative, and 'says' he can get more when his supply is exhausted.).
The gears were installed by a local guy, who has 30+ years of servicing GM vehicles, and many Corvettes. It cost me $425, including $60 for new speedo-recalibration parts, for the installation.
E-mail me if I can answer further questions!
Damn, George; you beat me to it AGAIN!!!!!