A030508 - OEIS

A030508

Graham-Sloane-type lower bound on the size of a ternary (n,3,8) constant-weight code.

16, 122, 549, 1837, 5069, 12203, 26510, 53141, 99840, 177811, 302759, 496128, 786545, 1211476, 1819136, 2670647, 3842461, 5429083, 7546084, 10333440, 13959209, 18623545, 24563096, 32055772, 41425920, 53049910, 67362149, 84861549, 106118453, 131782042, 162588234

(list; graph; refs; listen; history; text; internal format)

OFFSET

8,1

LINKS

Table of n, a(n) for n=8..38.

Mattias Svanstrom, A lower bound for ternary constant weight codes, IEEE Trans. on Information Theory, Vol. 43 (Sep. 1997), pp. 1630-1632.

FORMULA

a(n) = ceiling(binomial(n, w) * 2^w / (2*n + 1)) with w = 8.

MATHEMATICA

a[n_] := Ceiling[Binomial[n, 8] * 2^8 / (2*n + 1)]; Array[a, 40, 8] (* Amiram Eldar, Oct 31 2025 *)

CROSSREFS

Column k=8 of A390161.