Sometimes BIOSs will have a minimum version as a prerequisite (eg. needing v08 before you can go higher). This is usually because of a data structure change performed by that version of the BIOS, which newer BIOS' assume already happened.
Since, when trying to install V16, it tells you that you required at least V08, then having V08 should be sufficient to install any version after that (up to V16 anyway).
To find the driver, I took the string (from your link) that was offered for the A10 version:
DELL,DSK PROG,BIOS,T1600,,A10
Googled for DELL,DSK PROG,BIOS,T1600,,A08
...
Found:
DELL,DSK PROG,BIOS,T1600,A08
Precision T1600 system BIOS
Version A08, A08 (27 Apr 2012)
Fixes & Enhancements
Add 35W CPU fan table support