Information on Result #548076

There is no linear OA(5108, 227, F5, 82) (dual of [227, 119, 83]-code), because construction Y1 would yield
  1. OA(5107, 136, S5, 82), but
    • the linear programming bound shows that M ≥ 4 680614 732900 044285 630127 740921 339805 504137 246651 693367 478774 820966 691549 983806 908130 645751 953125 / 7377 156347 408094 956731 > 5107 [i]
  2. linear OA(5119, 227, F5, 91) (dual of [227, 108, 92]-code), but
    • discarding factors / shortening the dual code would yield linear OA(5119, 214, F5, 91) (dual of [214, 95, 92]-code), but
      • construction Y1 [i] would yield
        1. OA(5118, 142, S5, 91), but
          • the linear programming bound shows that M ≥ 227 290310 028755 622094 163273 225192 363202 339181 888847 417767 861303 072862 710905 610583 722591 400146 484375 / 5712 266942 976429 > 5118 [i]
        2. OA(595, 214, 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(5108, 227, F5, 2, 82) (dual of [(227, 2), 346, 83]-NRT-code) [i]Depth Reduction
2No linear OOA(5108, 227, F5, 3, 82) (dual of [(227, 3), 573, 83]-NRT-code) [i]
3No digital (26, 108, 227)-net over F5 [i]Extracting Embedded Orthogonal Array