A test tube comprises a tube body of unitary construction including an enclosed sidewall and an integral bottom that together define a tubular container having an open top. The bottom has a concave interior surface and a planar exterior surface upon which machine readable data is encoded within a multi-layered opaque coating that is deposited onto the planar exterior surface to uniquely identify the test tube. The machine readable data is preferably an open (i.e., non-proprietary) data matrix code. This code is applied to the test tube by depositing a multi-layer coating onto the planar exterior of the tube bottom. The multi-layer coating may include a first layer of opaque material that is deposited onto the planar exterior surface, and a second layer of opaque material that is deposited onto the first layer. The machine readable code is formed in the multi-layered coating by removing portions of the second layer.