Using assembly theory of strings of any natural radix $b$ we find some of their salient regularities. In particular, we show that the upper bound of the assembly index depends quantitatively on the radix $b$ and the longest length $N$ of a string that has the assembly index of $N-k$ is given by $N_{(N-1)}=b^2+b+1$ and by $N_{(N-k)}=b^2+b+2k$ for $2 \le k \le 9$. We also provide particular forms of such strings. Knowing the latter bound, we conjecture that the maximum assembly index of a string of length $N_{(N-2)} \le N \le N_{\text{max}}$ is given by $a_{\text{max}}^{(N,b)} = \lfloor N/2 \rfloor + b(b+1)/2$, where $N_{\text{max}} = 4b^4$ if $b$ is even and $N_{\text{max}} = 4(b^4+1)$ otherwise. For $k=1$ such odd length strings are nearly balanced and there are four such different strings if $b=2$ and seventy-two if $b=3$. We also show that each $k$ copies of an $n$-plet contained in a string decrease its assembly index at least by $k(n-1) - a$, where $a$ is the assembly index of this $n$-plet. We show that the minimum assembly depth satisfies $d_{\text{min}}^{(N)} = \left\lceil \log_2(N) \right\rceil$, for all $b$, and is the assembly depth of a maximum assembly index string. We define the depth index of a string (OEIS \href{https://oeis.org/A014701}{A014701} sequence) and conjecture that if it is equal to the minimum assembly index of this string then its assembly depth equals the minimum assembly depth, and otherwise equals the minimum assembly index. Since these results are also valid for $b=1$, assembly theory subsumes information theory.