You can print at 24x16", as long as you can find someone doing that size. Depending on the printer/medium, the higher the ppi, the better. Although, anything over 300 is usually just wasted information.
As long as the file size (dimensions) match your desired output (24x16) and the file is 300ppi (dpi) you should be right. Don't get too fussed by the actual file size, as this can differ depending upon the information contained in the file.