Asymptotic Gilbert–Varshamov bound (${\alpha }_q(\delta )\ge 1-H_q(\delta )$)

For $0\le \delta \le 1-1/q$, take logarithms of the Gilbert–Varshamov bound and apply the Hamming ball volume exponent. The Varshamov bound for linear codes gives the same achievable lower bound within linear codes for prime-power $q$.

// Target: algebra.bigb