I personally am a fan of duodecimal numbers, which have the advantages of hex but deal well with thirds also, a practical advantage. Both of these (and vingesimal, tregesimal and sexagesimal, too) contain the decimal and so solve naming problem.
I don't understand what you mean by "both of these". Duodecimal and hex don't solve the decimal naming problem, only the vingesimal, tregesimal and sexagesimal systems do.
There is another posibility - using the decimal system to write the numbers, but a kind of biquinary to name them in speach.
I met a kind of biquinary as the internal number representation in the IBM 650 computer, the first one I programmed in, but we didn't have access to it.
The advantage - we need to add just two new words, for 3 and 4, and the written numbers enable to use the
telephone numbers, SSNs, PINs, addresses and so on.
. It could be easy to learn and use, and reasonably short. Like "lukatu lukatu" for 77, "tu luka" for 25 and "wan ala ala" for 100
So I really would prefer this system - and go back to ternary only if there is an absolute tabu against new words, even two of them.
Thanks for your comments