Information on Result #547963

There is no linear OA(5132, 181, F5, 102) (dual of [181, 49, 103]-code), because construction Y1 would yield
  1. OA(5131, 147, S5, 102), but
    • the linear programming bound shows that M ≥ 249 236477 010921 693845 684281 987701 342304 847343 669838 056342 020625 628930 208250 721989 315934 479236 602783 203125 / 6 326951 585981 > 5131 [i]
  2. OA(549, 181, S5, 34), but
    • discarding factors would yield OA(549, 179, S5, 34), but
      • the linear programming bound shows that M ≥ 63101 461737 633561 195888 825311 804301 658299 627461 880998 569540 679454 803466 796875 / 3 393659 613629 526150 016067 267200 843099 664623 > 549 [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(5133, 182, F5, 103) (dual of [182, 49, 104]-code) [i]Truncation
2No linear OA(5134, 183, F5, 104) (dual of [183, 49, 105]-code) [i]
3No linear OOA(5133, 181, F5, 2, 103) (dual of [(181, 2), 229, 104]-NRT-code) [i]m-Reduction for OOAs
4No linear OOA(5134, 181, F5, 2, 104) (dual of [(181, 2), 228, 105]-NRT-code) [i]
5No linear OOA(5132, 181, F5, 2, 102) (dual of [(181, 2), 230, 103]-NRT-code) [i]Depth Reduction
6No linear OOA(5132, 181, F5, 3, 102) (dual of [(181, 3), 411, 103]-NRT-code) [i]
7No digital (30, 132, 181)-net over F5 [i]Extracting Embedded Orthogonal Array