Information on Result #547960

There is no linear OA(5127, 222, F5, 97) (dual of [222, 95, 98]-code), because construction Y1 would yield
  1. OA(5126, 150, S5, 97), but
    • the linear programming bound shows that M ≥ 36 026079 456021 401807 410154 480760 438768 372858 795374 723787 651793 517725 247462 113458 141175 215132 534503 936767 578125 / 2872 765687 918138 939304 > 5126 [i]
  2. OA(595, 222, S5, 72), but
    • discarding factors would yield OA(595, 145, S5, 72), but
      • the linear programming bound shows that M ≥ 681 594308 011084 642541 521008 533375 736738 792368 662881 901785 086204 561152 741164 839513 298410 490771 406244 903118 931688 368320 465087 890625 / 251 826768 360176 313961 784872 463983 728554 549094 621216 187309 311959 > 595 [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.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

ResultThis
result
only		Method
1No linear OOA(5127, 222, F5, 2, 97) (dual of [(222, 2), 317, 98]-NRT-code) [i]Depth Reduction
2No linear OOA(5127, 222, F5, 3, 97) (dual of [(222, 3), 539, 98]-NRT-code) [i]
3No digital (30, 127, 222)-net over F5 [i]Extracting Embedded Orthogonal Array