Information on Result #547865

There is no linear OA(4127, 183, F4, 91) (dual of [183, 56, 92]-code), because construction Y1 would yield
  1. OA(4126, 147, S4, 91), but
    • the linear programming bound shows that M ≥ 340456 058530 442352 522099 250356 400004 547517 225644 691214 440472 273914 376101 952655 553716 027392 / 33 253308 357995 > 4126 [i]
  2. OA(456, 183, S4, 36), but
    • discarding factors would yield OA(456, 179, S4, 36), but
      • the linear programming bound shows that M ≥ 31 511442 125419 258293 449040 901884 044621 696169 017943 480590 506370 111897 600000 / 5839 126320 766662 475522 447173 784673 305301 > 456 [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(4127, 183, F4, 2, 91) (dual of [(183, 2), 239, 92]-NRT-code) [i]Depth Reduction
2No linear OOA(4127, 183, F4, 3, 91) (dual of [(183, 3), 422, 92]-NRT-code) [i]
3No digital (36, 127, 183)-net over F4 [i]Extracting Embedded Orthogonal Array