Information on Result #547853

There is no linear OA(4112, 216, F4, 79) (dual of [216, 104, 80]-code), because construction Y1 would yield
  1. OA(4111, 143, S4, 79), but
    • the linear programming bound shows that M ≥ 237 737030 554406 831140 331461 504711 505012 046426 036658 538250 578745 045288 416863 000860 792142 692352 / 26 111742 312416 213213 385625 > 4111 [i]
  2. OA(4104, 216, S4, 73), but
    • discarding factors would yield OA(4104, 150, S4, 73), but
      • the linear programming bound shows that M ≥ 32 028783 264027 932827 838658 827950 132017 443030 031565 779091 184319 519613 927802 631343 679332 066747 830675 439616 / 70932 376441 373736 310653 589982 582096 950125 > 4104 [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(4112, 216, F4, 2, 79) (dual of [(216, 2), 320, 80]-NRT-code) [i]Depth Reduction
2No linear OOA(4112, 216, F4, 3, 79) (dual of [(216, 3), 536, 80]-NRT-code) [i]
3No digital (33, 112, 216)-net over F4 [i]Extracting Embedded Orthogonal Array
4No linear OA(4108, 220, F4, 76) (dual of [220, 112, 77]-code) [i]Construction Y1 (Bound)