MinT - Information on Result #1204212

Information on Result #1204212

Digital (33, 64, 1093)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁶⁴, 1093, F₁₂₈, 31, 31) (dual of [(1093, 31), 33819, 32]-NRT-code), using

OOA 15-folding and stacking with additional row [i] based on linear OA(128⁶⁴, 16396, F₁₂₈, 31) (dual of [16396, 16332, 32]-code), using
- constructionÂ X applied to C([0,15]) âŠ‚ C([0,13]) [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(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]
  3. linear OA(128³, 11, F₁₂₈, 3) (dual of [11, 8, 4]-code or 11-arc in PG(2,128) or 11-cap in PG(2,128)), using
    - discarding factors / shortening the dual code based on linear OA(128³, 128, F₁₂₈, 3) (dual of [128, 125, 4]-code or 128-arc in PG(2,128) or 128-cap in PG(2,128)), using
      - Reedâ€“Solomon code RS(125,128) [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, 64, 1093)-net over F₁₂₈	[i]	t-Expansion
2	Digital (34, 65, 1093)-net over F₁₂₈	[i]	Net Duplication
3	Digital (35, 66, 1093)-net over F₁₂₈	[i]
4	Digital (36, 67, 1093)-net over F₁₂₈	[i]
5	Digital (37, 68, 1093)-net over F₁₂₈	[i]
6	Digital (38, 69, 1093)-net over F₁₂₈	[i]
7	Digital (33, 63, 1093)-net over F₁₂₈	[i]	m-Reduction