To be able to reversibly encode an N-trit ternary number into an M-bit binary number, the number of possible N-trit numbers must be less or equal to the number

To be able to reversibly encode an N-trit ternary number into an M-bit binary number, the number of possible N-trit numbers must be less or equal to the number of possible M-bit binary numbers. Otherwise there would be two input ternary numbers that would map to the the same binary number (pigeonhole principle). Which means that 3^N <= 2^M. 3^N <= 2^M log(3^N) <= log(2^M) N*log(3) <= M*log(2) log(3)/log(2) <= M/N where M/N is the bits per ternary digit.