Information on Result #547868

There is no linear OA(4130, 186, F4, 93) (dual of [186, 56, 94]-code), because construction Y1 would yield
  1. OA(4129, 150, S4, 93), but
    • the linear programming bound shows that M ≥ 334 695053 805711 397561 375492 015414 168229 977994 664798 746384 442171 245301 199155 917928 366979 678208 / 643 455449 300513 > 4129 [i]
  2. OA(456, 186, 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(4130, 186, F4, 2, 93) (dual of [(186, 2), 242, 94]-NRT-code) [i]Depth Reduction
2No linear OOA(4130, 186, F4, 3, 93) (dual of [(186, 3), 428, 94]-NRT-code) [i]
3No digital (37, 130, 186)-net over F4 [i]Extracting Embedded Orthogonal Array