Information on Result #547757

There is no linear OA(3109, 210, F3, 67) (dual of [210, 101, 68]-code), because construction Y1 would yield
  1. OA(3108, 148, S3, 67), but
    • the linear programming bound shows that M ≥ 78025 871208 892313 168943 730744 500191 908721 562995 779216 058480 164902 383334 112359 / 18 249022 055379 161691 813025 > 3108 [i]
  2. OA(3101, 210, S3, 62), but
    • discarding factors would yield OA(3101, 149, S3, 62), but
      • the linear programming bound shows that M ≥ 8233 296774 908639 119144 152333 781856 470978 676092 263597 209204 295760 374352 043379 617679 / 5157 240609 884987 743181 747606 796875 > 3101 [i]

Mode: Bound (linear).

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Compare with Markus Grassl’s online database of code parameters.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1No linear OOA(3109, 210, F3, 2, 67) (dual of [(210, 2), 311, 68]-NRT-code) [i]Depth Reduction
2No linear OOA(3109, 210, F3, 3, 67) (dual of [(210, 3), 521, 68]-NRT-code) [i]
3No linear OOA(3109, 210, F3, 4, 67) (dual of [(210, 4), 731, 68]-NRT-code) [i]
4No linear OA(3103, 212, F3, 63) (dual of [212, 109, 64]-code) [i]Construction Y1 (Bound)