MinT - Information on Result #1207947

Information on Result #1207947

Digital (168, 178, 6723845)-net over F₃, using (u,Â u+v)-construction based on

digital (25, 30, 12965)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3³⁰, 12965, F₃, 5, 5) (dual of [(12965, 5), 64795, 6]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OOA(3³⁰, 12966, F₃, 2, 5) (dual of [(12966, 2), 25902, 6]-NRT-code), using
    - (u,Â u+v)-construction [i] based on
      1. linear OOA(3², 4, F₃, 2, 2) (dual of [(4, 2), 6, 3]-NRT-code), using
        extended Reedâ€“Solomon NRT-code RS_e(2;6,3) [i]
      2. linear OOA(3²⁸, 12962, F₃, 2, 5) (dual of [(12962, 2), 25896, 6]-NRT-code), using
        OOA 2-folding [i] based on linear OA(3²⁸, 25924, F₃, 5) (dual of [25924, 25896, 6]-code), using
        trace code [i] based on linear OA(81⁷, 6481, F₈₁, 5) (dual of [6481, 6474, 6]-code), using
        a code by Danev and Olsson [i]
digital (138, 148, 6710880)-net over F₃, using
- trace code for nets [i] based on digital (27, 37, 1677720)-net over F₈₁, using
  - net defined by OOA [i] based on linear OOA(81³⁷, 1677720, F₈₁, 10, 10) (dual of [(1677720, 10), 16777163, 11]-NRT-code), using
    - OA 5-folding and stacking [i] based on linear OA(81³⁷, 8388600, F₈₁, 10) (dual of [8388600, 8388563, 11]-code), using
      - discarding factors / shortening the dual code based on linear OA(81³⁷, large, F₈₁, 10) (dual of [large, large−37, 11]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]

Mode: Constructive and linear.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹⁷⁸, 6723845, F₃, 5, 10) (dual of [(6723845, 5), 33619047, 11]-NRT-code)	[i]		Extracting Embedded OOA