MinT - Information on Result #3163368

Information on Result #3163368

Digital (139, 144, large)-net over F₃, using 4 times m-reduction based on digital (139, 148, large)-net over F₃, using

trace code for nets [i] based on digital (28, 37, 2097231)-net over F₈₁, using
- net defined by OOA [i] based on linear OOA(81³⁷, 2097231, F₈₁, 12, 9) (dual of [(2097231, 12), 25166735, 10]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(81³⁷, 2097232, F₈₁, 4, 9) (dual of [(2097232, 4), 8388891, 10]-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(81³³, 2097150, F₈₁, 4, 9) (dual of [(2097150, 4), 8388567, 10]-NRT-code), using
        OOA 4-folding [i] based on linear OA(81³³, 8388600, F₈₁, 9) (dual of [8388600, 8388567, 10]-code), using
        discarding factors / shortening the dual code based on linear OA(81³³, large, F₈₁, 9) (dual of [large, large−33, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [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 (140, 144, large)-net over F₃	[i]		t-Expansion
2	Digital (141, 144, large)-net over F₃	[i]		t-Expansion