Storage-efficiency conjecture for load-balancing modulation codes

Let $l$ be the number of choices in the load-balancing modulation code, let $q$ be the number of charge levels, let $n$ be the number of memory cells, and let $k$ denote the message-length parameter. The storage efficiency is denoted by $\gamma$.

Storage-efficiency conjecture. If $l=2$ and $q-1=c\ln n$, then the load-balancing modulation code has storage efficiency $\gamma=k$ with probability $1-o(1)$ as $n\rightarrow\infty$. If $q-1=c$, the storage efficiency is

$$\gamma=\frac{c\ln 2}{\ln\ln n}k$$

with probability $1-o(1)$.

The conjecture asserts that the ball-loading performance of this modulation code matches that of the random-loading algorithm with two random choices. The supplied source gives no resolution status, so it is recorded as open.