MinT - Information on Result #3162498

Information on Result #3162498

Digital (124, 129, large)-net over F₃, using 3 times m-reduction based on digital (124, 132, large)-net over F₃, using

trace code for nets [i] based on digital (25, 33, 2097231)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81³³, 2097231, F₈₁, 12, 8) (dual of [(2097231, 12), 25166739, 9]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(81³³, 2097232, F₈₁, 4, 8) (dual of [(2097232, 4), 8388895, 9]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(81⁴, 82, F₈₁, 4, 4) (dual of [(82, 4), 324, 5]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(4;324,81) [i]
      2. linear OOA(81²⁹, 2097150, F₈₁, 4, 8) (dual of [(2097150, 4), 8388571, 9]-NRT-code), using
        OOA 4-folding [i] based on linear OA(81²⁹, 8388600, F₈₁, 8) (dual of [8388600, 8388571, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(81²⁹, large, F₈₁, 8) (dual of [large, large−29, 9]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (125, 129, large)-net over F₃	[i]		t-Expansion
2	Digital (126, 129, large)-net over F₃	[i]		t-Expansion