On asymptotic bases and minimal asymptotic bases

Let $\mathbb {N}=\{0,1,2,\ldots \}$ and $A\subset \mathbb {N}$. $h\geq 2$ let $r_h(A,n)=\sharp \{ (a_1,\ldots ,a_h) \in A^{h}: a_1+\cdots +a_h=n\}.$ The set $A$ is called an asymptotic basis of order $h$ if $r_h(A,n)\geq 1$ for all sufficiently la