These factories share n, k and d but prepare different magic states. No CNOT circuit with S, Z and CZ corrections turns one of these gates into another.
Nearest lengths with the same k and d: [\![62,\,7,\,3]\!] · [\![61,\,7,\,3]\!] · [\![65,\,7,\,3]\!] · [\![60,\,7,\,3]\!] · [\![59,\,7,\,3]\!] · [\![55,\,7,\,3]\!] · [\![48,\,7,\,3]\!] · [\![79,\,7,\,3]\!] · [\![44,\,7,\,3]\!] · [\![43,\,7,\,3]\!] · [\![84,\,7,\,3]\!] · [\![91,\,7,\,3]\!]