MinT - Information on Result #1204242

Information on Result #1204242

Digital (35, 70, 964)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁷⁰, 964, F₁₂₈, 35, 35) (dual of [(964, 35), 33670, 36]-NRT-code), using

OOA 17-folding and stacking with additional row [i] based on linear OA(128⁷⁰, 16389, F₁₂₈, 35) (dual of [16389, 16319, 36]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁷⁰, 16390, F₁₂₈, 35) (dual of [16390, 16320, 36]-code), using
  - constructionÂ X applied to C([0,17]) âŠ‚ C([0,16]) [i] based on
    1. linear OA(128⁶⁹, 16385, F₁₂₈, 35) (dual of [16385, 16316, 36]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,17], and minimum distance dÂ â‰¥ |{−17,−16,…,17}|+1Â =Â 36 (BCH-bound) [i]
    2. linear OA(128⁶⁵, 16385, F₁₂₈, 33) (dual of [16385, 16320, 34]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,16], and minimum distance dÂ â‰¥ |{−16,−15,…,16}|+1Â =Â 34 (BCH-bound) [i]
    3. linear OA(128¹, 5, F₁₂₈, 1) (dual of [5, 4, 2]-code), using
      - discarding factors / shortening the dual code based on linear OA(128¹, s, F₁₂₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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 (36, 70, 964)-net over F₁₂₈	[i]	t-Expansion
2	Digital (36, 71, 964)-net over F₁₂₈	[i]	Net Duplication
3	Digital (37, 72, 964)-net over F₁₂₈	[i]
4	Digital (38, 73, 964)-net over F₁₂₈	[i]
5	Digital (39, 74, 964)-net over F₁₂₈	[i]
6	Digital (40, 75, 964)-net over F₁₂₈	[i]
7	Digital (35, 69, 964)-net over F₁₂₈	[i]	m-Reduction
8	(63, 98, 964)-net in base 32	[i]	Base Change