Information on Result #547961

There is no linear OA(5128, 214, F5, 98) (dual of [214, 86, 99]-code), because construction Y1 would yield
  1. OA(5127, 149, S5, 98), but
    • the linear programming bound shows that M ≥ 5193 361256 119414 558729 044685 549653 156610 735015 094949 701472 602202 230455 237241 812938 009388 744831 085205 078125 / 69869 528585 224173 > 5127 [i]
  2. OA(586, 214, S5, 65), but
    • discarding factors would yield OA(586, 145, S5, 65), but
      • the linear programming bound shows that M ≥ 1 681971 586304 181223 187907 190141 264188 172812 749344 276629 843014 476462 881651 126808 966524 933987 666420 440086 867329 609762 499671 015636 681116 117777 216867 334999 506056 192331 016063 690185 546875 / 1 235197 506395 108210 300700 030853 409382 253498 637886 138574 180390 146599 149915 868081 543662 842688 306834 854616 250416 282850 014131 > 586 [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 OA(5129, 215, F5, 99) (dual of [215, 86, 100]-code) [i]Truncation
2No linear OOA(5129, 214, F5, 2, 99) (dual of [(214, 2), 299, 100]-NRT-code) [i]m-Reduction for OOAs
3No linear OOA(5128, 214, F5, 2, 98) (dual of [(214, 2), 300, 99]-NRT-code) [i]Depth Reduction
4No linear OOA(5128, 214, F5, 3, 98) (dual of [(214, 3), 514, 99]-NRT-code) [i]
5No digital (30, 128, 214)-net over F5 [i]Extracting Embedded Orthogonal Array