MinT - Information on Result #1204126

Information on Result #1204126

Digital (33, 60, 1262)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁶⁰, 1262, F₁₂₈, 27, 27) (dual of [(1262, 27), 34014, 28]-NRT-code), using

OOA 13-folding and stacking with additional row [i] based on linear OA(128⁶⁰, 16407, F₁₂₈, 27) (dual of [16407, 16347, 28]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁶⁰, 16408, F₁₂₈, 27) (dual of [16408, 16348, 28]-code), using
  - constructionÂ X applied to C([0,13]) âŠ‚ C([0,9]) [i] based on
    1. linear OA(128⁵³, 16385, F₁₂₈, 27) (dual of [16385, 16332, 28]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,13], and minimum distance dÂ â‰¥ |{−13,−12,…,13}|+1Â =Â 28 (BCH-bound) [i]
    2. linear OA(128³⁷, 16385, F₁₂₈, 19) (dual of [16385, 16348, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
    3. linear OA(128⁷, 23, F₁₂₈, 7) (dual of [23, 16, 8]-code or 23-arc in PG(6,128)), using
      - discarding factors / shortening the dual code based on linear OA(128⁷, 128, F₁₂₈, 7) (dual of [128, 121, 8]-code or 128-arc in PG(6,128)), using
        Reedâ€“Solomon code RS(121,128) [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 (34, 60, 1262)-net over F₁₂₈	[i]	t-Expansion
2	Digital (34, 61, 1262)-net over F₁₂₈	[i]	Net Duplication
3	Digital (35, 62, 1262)-net over F₁₂₈	[i]
4	Digital (36, 63, 1262)-net over F₁₂₈	[i]
5	Digital (33, 59, 1262)-net over F₁₂₈	[i]	m-Reduction
6	(43, 70, 1262)-net in base 64	[i]	Base Change