Did Ahmes find the best expansions for 2/n?

A couple of years back I was discussing the Rhind Mathematical Papyrus (RMP). It includes a table expressing as a sum $$\frac1{a_1}+\frac1{a_2}+\dots+\frac1{a_k} $$ fractions with numerator 1 (“unit fractions”). I said: Getting the table of good-quality representations of is not trivial, and requires searching, number theory, and some trial and error. It's not at all clear that . Today I wondered: did Ahmes (the author) have the best possible expansions for all the values, or w...