It must be over a year since I last looked at the IANA IDN tables and they have grown massively in that time ➜ iana.org/domains/idn-tables

Some observations: I will use Verisignʼs Japanese .コム (transliteration of .com)

There is .コム Japanese, which is LDH (ASCII Letters, Digits, Hyphen) + Hiragana + Katakana + a heap of Han
There is .コム Hiragana, which is DH + Hiragana
There is .コム Katakana, which is DH + Katakana
There is .コム Han, which is DH + a heap of Han

André Schappo