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.
Same n and k at other distances: [\![60,\,6,\,2]\!]
Nearest lengths with the same k and d: [\![59,\,6,\,3]\!] · [\![58,\,6,\,3]\!] · [\![62,\,6,\,3]\!] · [\![63,\,6,\,3]\!] · [\![56,\,6,\,3]\!] · [\![55,\,6,\,3]\!] · [\![66,\,6,\,3]\!] · [\![67,\,6,\,3]\!] · [\![52,\,6,\,3]\!] · [\![68,\,6,\,3]\!] · [\![51,\,6,\,3]\!] · [\![70,\,6,\,3]\!]