I think the optimal base is actually the natural log e, or about 2.71. I saw a derivation of this before but can't find the reference. Ternary actually comes ab

I think the optimal base is actually the natural log e, or about 2.71. I saw a derivation of this before but can't find the reference. Ternary actually comes about a bit better from an information density standpoint, but all the other points you made about difficulties with base 3 and benefits of base 2 still stand.