Information on Result #547874

There is no linear OA(4137, 238, F4, 99) (dual of [238, 101, 100]-code), because construction Y1 would yield
  1. linear OA(4136, 167, F4, 99) (dual of [167, 31, 100]-code), but
    • construction Y1 [i] would yield
      1. OA(4135, 149, S4, 99), but
        • the linear programming bound shows that M ≥ 2 040610 487096 181427 758937 498317 933435 839690 422249 792187 355243 784188 300883 648114 289820 041216 / 970 822125 > 4135 [i]
      2. OA(431, 167, S4, 18), but
  2. OA(4101, 238, S4, 71), but
    • discarding factors would yield OA(4101, 146, S4, 71), but
      • the linear programming bound shows that M ≥ 780 391601 299222 805405 564977 076901 757366 079162 890923 638174 195116 932617 997552 007423 809669 824512 / 113 932691 512033 126701 906109 976895 > 4101 [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(4137, 238, F4, 2, 99) (dual of [(238, 2), 339, 100]-NRT-code) [i]Depth Reduction
2No linear OOA(4137, 238, F4, 3, 99) (dual of [(238, 3), 577, 100]-NRT-code) [i]
3No digital (38, 137, 238)-net over F4 [i]Extracting Embedded Orthogonal Array