Information on Result #547755

There is no linear OA(3106, 207, F3, 65) (dual of [207, 101, 66]-code), because construction Y1 would yield
  1. OA(3105, 145, S3, 65), but
    • the linear programming bound shows that M ≥ 2672 696874 555113 070277 370361 668201 700430 711731 822164 429384 303409 602728 450455 / 21 255599 528627 666044 419356 > 3105 [i]
  2. OA(3101, 207, 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(3106, 207, F3, 2, 65) (dual of [(207, 2), 308, 66]-NRT-code) [i]Depth Reduction
2No linear OOA(3106, 207, F3, 3, 65) (dual of [(207, 3), 515, 66]-NRT-code) [i]