1. A computer-implemented method for registering multilingual domain names that include non-ASCII characters, the method comprising: receiving a request from a user to register a multilingual domain name in a top-level domain (TLD), the multilingual domain name having a specified second-level domain name portion that is composed of non-ASCII characters from a specified non-ASCII character set, each character in the specified character set having an associated numeric value, the second-level domain name portion indicated in the received request by a sequence of the numeric values that are associated with the non-ASCII characters of the second-level domain name portion; generating an ASCII-Compatible Encoding (ACE) for the specified second-level domain name portion based on the specified character set and the indicated numeric sequence for the second-level domain name portion; constructing an ASCII domain name whose second-level domain name portion is the generated ACE and whose top-level domain name portion is the TLD; determining whether the constructed ASCII domain name is available to be registered in the TLD and whether the indicated numeric sequence has already been reserved for another multilingual domain name registered in the TLD; and when it is determined that the constructed ASCII domain name is available to be registered and that the indicated numeric sequence has not been reserved, registering the mutilingual domain name in the TLD by, generating multiple distinct numeric sequence variants as equivalents for the specified second-level domain name portion of the multilingual domain name, each generated numeric sequence variant consisting of a sequence of numeric values; and reserving the generated numeric sequence variants for the multilingual domain name.