In the book: Introduction to coding by Roth, the author makes a claim that the integer effect (which I understood it as being the rounding effect) would phase out as we aggregate over an infinite number of transmissions, while I think nothing would change (since eventually l would be factored out). The following shows the author words
Let us show an example. We will let $F=3$, so we have an alphabet of $3$ symbols. If we want to send one of $16$ messages, we have to send $\lceil \log_3 (16) \rceil=3$ symbols. This is a waste, we can actually send $3^3=27$ different messages. $\log_3(16) \approx 2.52$, so we are wasting about a half a symbol or $\frac 16$ of our message. If we want to send one of $2^{16}=65536$ messages, we need to send $\lceil \log_3 (65536) \rceil=3$ symbols. We need $11$ symbols and waste $0.91$ of one because the log is just over $10$. The fraction wasted is $\frac {0.91}{11} \approx \frac 1{12}$ of the message. As the number of messages increases, the wasted symbols are bounded above by $1$, so the fraction wasted goes down with the number of symbols required.