MinT - Information on Result #3198673

Information on Result #3198673

Digital (163, 171, large)-net over F₃, using t-expansion based on digital (162, 171, large)-net over F₃, using

trace code for nets [i] based on digital (48, 57, 4194300)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27⁵⁷, 4194300, F₂₇, 10, 9) (dual of [(4194300, 10), 41942943, 10]-NRT-code), using
  - OOA 2-folding and stacking with additional row [i] based on linear OOA(27⁵⁷, 8388601, F₂₇, 2, 9) (dual of [(8388601, 2), 16777145, 10]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(27⁵⁷, 8388602, F₂₇, 2, 9) (dual of [(8388602, 2), 16777147, 10]-NRT-code), using
      - (u,Â u+v)-construction [i] based on
        linear OOA(27¹⁶, 4194301, F₂₇, 2, 4) (dual of [(4194301, 2), 8388586, 5]-NRT-code), using
        OOA 2-folding [i] based on linear OA(27¹⁶, 8388602, F₂₇, 4) (dual of [8388602, 8388586, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(27¹⁶, large, F₂₇, 4) (dual of [large, large−16, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 27⁵âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
        linear OOA(27⁴¹, 4194301, F₂₇, 2, 9) (dual of [(4194301, 2), 8388561, 10]-NRT-code), using
        OOA 2-folding [i] based on linear OA(27⁴¹, 8388602, F₂₇, 9) (dual of [8388602, 8388561, 10]-code), using
        discarding factors / shortening the dual code based on linear OA(27⁴¹, large, F₂₇, 9) (dual of [large, large−41, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’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		Method
1	Digital (164, 172, large)-net over F₃	[i]	Net Duplication
2	Digital (165, 173, large)-net over F₃	[i]
3	Digital (166, 174, large)-net over F₃	[i]
4	Digital (167, 175, large)-net over F₃	[i]
5	Digital (168, 176, large)-net over F₃	[i]
6	Digital (169, 177, large)-net over F₃	[i]
7	Digital (170, 178, large)-net over F₃	[i]
8	Digital (171, 179, large)-net over F₃	[i]
9	Digital (172, 180, large)-net over F₃	[i]
10	Digital (173, 181, large)-net over F₃	[i]