On optimal linear codes over F5

Let nq(k, d) be the smallest integer n for which there exists an [n, k, d]q code for given q, k, d. It is known that n8(4, d) = ∑3 i=0 ⌈ d/8i ⌉ for all d ≥ 833. As a continuation of Jones et al. [Electronic J. Combinatorics 13 (2006), #R43], we determine n8(4, d) for 117 values of d with 113 ≤ d ≤ 832 and give upper and lower bounds on n8(4, d) for other d using geometric methods and some extension theorems for linear codes.