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,\,6,\,3]\!] · [\![60,\,6,\,3]\!] · [\![66,\,6,\,3]\!] · [\![59,\,6,\,3]\!] · [\![67,\,6,\,3]\!] · [\![58,\,6,\,3]\!] · [\![68,\,6,\,3]\!] · [\![56,\,6,\,3]\!] · [\![70,\,6,\,3]\!] · [\![55,\,6,\,3]\!] · [\![71,\,6,\,3]\!] · [\![52,\,6,\,3]\!]