Your sax is very likely a "stencil" instrument, made by one of the major manufacturers such as Conn, Martin, or Buescher under contract. Serial numbers on such horns are usually impossible to trace. Knowledgeable people can usually determine the manufacturer by noting design elements common to your horn and the manufacturer's regular output, and can at least narrow the date range somewhat, since these horns usually had some, but not all, of the standard output's features at the time of manufacture.