Information on Result #547869

There is no linear OA(4131, 186, F4, 94) (dual of [186, 55, 95]-code), because construction Y1 would yield
  1. OA(4130, 151, S4, 94), but
    • 1 times truncation [i] would yield 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(455, 186, S4, 35), but
    • the linear programming bound shows that M ≥ 2227 845699 810146 058122 102603 602007 534656 013828 852609 458125 647380 480000 / 1 700436 329479 757404 993871 394563 863537 > 455 [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(4131, 186, F4, 2, 94) (dual of [(186, 2), 241, 95]-NRT-code) [i]Depth Reduction
2No linear OOA(4131, 186, F4, 3, 94) (dual of [(186, 3), 427, 95]-NRT-code) [i]