Information on Result #547867

There is no linear OA(4128, 181, F4, 92) (dual of [181, 53, 93]-code), because construction Y1 would yield
  1. OA(4127, 147, S4, 92), but
    • the linear programming bound shows that M ≥ 1349 953590 687270 246179 045330 695244 563410 842122 028765 631284 937718 372400 148416 386214 476266 864640 / 41158 876076 530201 > 4127 [i]
  2. OA(453, 181, S4, 34), but
    • discarding factors would yield OA(453, 172, S4, 34), but
      • the linear programming bound shows that M ≥ 123466 093718 521640 819257 910588 141484 804246 154591 951516 762688 716800 / 1516 591174 436793 940747 804532 901223 > 453 [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(4128, 181, F4, 2, 92) (dual of [(181, 2), 234, 93]-NRT-code) [i]Depth Reduction
2No linear OOA(4128, 181, F4, 3, 92) (dual of [(181, 3), 415, 93]-NRT-code) [i]
3No digital (36, 128, 181)-net over F4 [i]Extracting Embedded Orthogonal Array