Compact symmetric solutions to the postage stamp problem

We derive lower and upper bounds on possible growth rates of certain sets of positive integers $A_k=\{1=a_1<a_2<\mathrm{.}\mathrm{.}\mathrm{.}<a_k\}$ such that all integers $n\in \{0,1,2,\mathrm{.}\mathrm{.}\mathrm{.},k{a}_k\}$ can be represented as a sum of no more than $k$ elements of $A_k$, with repetition.