MinT - Information on Result #1204214

Information on Result #1204214

Digital (39, 70, 1094)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁷⁰, 1094, F₁₂₈, 31, 31) (dual of [(1094, 31), 33844, 32]-NRT-code), using

OOA 15-folding and stacking with additional row [i] based on linear OA(128⁷⁰, 16411, F₁₂₈, 31) (dual of [16411, 16341, 32]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁷⁰, 16414, F₁₂₈, 31) (dual of [16414, 16344, 32]-code), using
  - constructionÂ X applied to C([0,15]) âŠ‚ C([0,10]) [i] based on
    1. linear OA(128⁶¹, 16385, F₁₂₈, 31) (dual of [16385, 16324, 32]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,15], and minimum distance dÂ â‰¥ |{−15,−14,…,15}|+1Â =Â 32 (BCH-bound) [i]
    2. linear OA(128⁴¹, 16385, F₁₂₈, 21) (dual of [16385, 16344, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
    3. linear OA(128⁹, 29, F₁₂₈, 9) (dual of [29, 20, 10]-code or 29-arc in PG(8,128)), using
      - discarding factors / shortening the dual code based on linear OA(128⁹, 128, F₁₂₈, 9) (dual of [128, 119, 10]-code or 128-arc in PG(8,128)), using
        Reedâ€“Solomon code RS(119,128) [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		Method
1	Digital (40, 70, 1094)-net over F₁₂₈	[i]	t-Expansion
2	Digital (40, 71, 1094)-net over F₁₂₈	[i]	Net Duplication
3	Digital (41, 72, 1094)-net over F₁₂₈	[i]
4	Digital (42, 73, 1094)-net over F₁₂₈	[i]
5	Digital (39, 69, 1094)-net over F₁₂₈	[i]	m-Reduction