Information on Result #547856

There is no linear OA(4116, 209, F4, 82) (dual of [209, 93, 83]-code), because construction Y1 would yield
  1. OA(4115, 144, S4, 82), but
    • the linear programming bound shows that M ≥ 1 809384 318048 793962 648861 468486 632853 295185 954954 708490 452357 715816 889075 089941 955770 056704 / 950 296664 568803 286553 > 4115 [i]
  2. OA(493, 209, S4, 65), but
    • discarding factors would yield OA(493, 148, S4, 65), but
      • the linear programming bound shows that M ≥ 31410 303083 703049 377310 817051 099884 117194 259592 068916 365914 768905 433278 533937 431277 207276 796100 647129 523955 480347 541504 / 271 727597 647736 395513 057790 697511 115852 689190 837400 656430 005393 > 493 [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(4116, 209, F4, 2, 82) (dual of [(209, 2), 302, 83]-NRT-code) [i]Depth Reduction
2No linear OOA(4116, 209, F4, 3, 82) (dual of [(209, 3), 511, 83]-NRT-code) [i]
3No digital (34, 116, 209)-net over F4 [i]Extracting Embedded Orthogonal Array