The low-power error-correcting cooling code density conjecture

Let $t$ and $w$ be fixed, and let $C(n,t,w,w-2)$ denote the maximum size of an $(n,t,w,w-2)$-LPECC code. Assume

$$(t+1)w(w-1)<(w+t)(w+t-1).$$

Low-power error-correcting cooling code density conjecture. Under this condition,

$$\lim_{n\to\infty}\frac{C(n,t,w,w-2)}{n^2}=\frac{1}{(t+1)w(w-1)},$$

or, more strongly,

$$C(n,t,w,w-2)=\left\lfloor\frac{(n+1)n}{(t+1)w(w-1)}\right\rfloor$$

for infinitely many $n$ with fixed $w$ and $t$. The conjecture proposes that the lower-bound density is asymptotically optimal, and that the stronger exact value is attained infinitely often; the source gives no resolution.