Information on Result #547858

There is no linear OA(4119, 216, F4, 84) (dual of [216, 97, 85]-code), because construction Y1 would yield
  1. OA(4118, 148, S4, 84), but
    • the linear programming bound shows that M ≥ 7301 270043 157677 378834 968797 352546 115167 116693 516048 447726 743341 396059 833062 672218 026684 710912 / 58934 105814 768105 796875 > 4118 [i]
  2. OA(497, 216, S4, 68), but
    • discarding factors would yield OA(497, 147, S4, 68), but
      • the linear programming bound shows that M ≥ 53191 285542 209075 945504 006887 276132 854449 205165 228826 719771 521828 218168 917559 533017 381886 236463 273092 752842 577445 650432 / 2 089901 251760 098724 970145 084401 522230 137171 459432 895605 490625 > 497 [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(4119, 216, F4, 2, 84) (dual of [(216, 2), 313, 85]-NRT-code) [i]Depth Reduction
2No linear OOA(4119, 216, F4, 3, 84) (dual of [(216, 3), 529, 85]-NRT-code) [i]
3No digital (35, 119, 216)-net over F4 [i]Extracting Embedded Orthogonal Array