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