Information on Result #547857

There is no linear OA(4117, 203, F4, 83) (dual of [203, 86, 84]-code), because construction Y1 would yield
  1. OA(4116, 143, S4, 83), but
    • the linear programming bound shows that M ≥ 247019 501721 767325 521677 985124 228608 567579 718666 161103 517597 971229 442510 874624 631519 576064 / 26 250606 256753 373495 > 4116 [i]
  2. OA(486, 203, S4, 60), but
    • discarding factors would yield OA(486, 145, S4, 60), but
      • the linear programming bound shows that M ≥ 70 960269 863126 606518 991667 215730 563206 075021 389069 425781 018295 735734 868068 159984 954116 355960 140231 669388 460318 751919 101866 886859 928826 023614 873600 / 11532 795767 709720 554647 969916 716816 544438 820799 421172 775769 384715 477815 805045 795696 528849 736837 > 486 [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(4117, 203, F4, 2, 83) (dual of [(203, 2), 289, 84]-NRT-code) [i]Depth Reduction
2No linear OOA(4117, 203, F4, 3, 83) (dual of [(203, 3), 492, 84]-NRT-code) [i]
3No digital (34, 117, 203)-net over F4 [i]Extracting Embedded Orthogonal Array