It seems a bit difficult to get exact data on resolution preferred by billboard printers. But one site
had this to say:
For our 300 DPI output vinyl banner printing, we need a raster file resolution of 72 DPI at actual size. For instance, a 6' x 20' vinyl print could be set up at 6" x 20" @ 864 DPI, which is equivalent to 6' x 20' @ 72 DPI.
For our 70 DPI printed billboards, we need a raster file resolution of 25 DPI at actual size. For instance, a 14' x 48' billboard could be set up at 14" x 48" @ 300 DPI, which is equivalent to 14' x 48' @ 25 DPI.
These resolutions work well, but you may add more resolution if you wish. Our general rule of thumb for resolution is the more resolution you put into the system, the more you will get out of the system.
Of course, you need not worry about the resolution for vector graphics from programs such as Adobe Illustrator. It is wise to keep in mind that the DPI suggestions above still apply to raster images placed in vectorized graphics.
This PDF also has some artwork specs for billboards:
There apeared to be some variation for resolution required, but most seemed to be in the region I quoted in the earlier post, although some were lower, such as 20-30 dpi. Most recommended setting up the file in the ratio of 0.5" or 1" for each 1' of final size. And using 300 dpi images means that the final resolution will be 50 dpi or 25dpi respectively.