Positive-rate coding bound below one-quarter crossover
= Positive-rate coding bound below one-quarter crossover
If $p<1/4$, choose $p<\delta<1/4$. Binary codes of relative minimum distance above $2\delta$ have positive asymptotic rate by a greedy packing bound, and nearest-codeword decoding fails only when more than $\delta n$ channel errors occur. That probability tends to zero.