MinT - Information on Result #1203688

Information on Result #1203688

Digital (19, 36, 2049)-net over F₁₂₈, using net defined by OOA based on linear OOA(128³⁶, 2049, F₁₂₈, 17, 17) (dual of [(2049, 17), 34797, 18]-NRT-code), using

OOA 8-folding and stacking with additional row [i] based on linear OA(128³⁶, 16393, F₁₂₈, 17) (dual of [16393, 16357, 18]-code), using
- discarding factors / shortening the dual code based on linear OA(128³⁶, 16396, F₁₂₈, 17) (dual of [16396, 16360, 18]-code), using
  - constructionÂ X applied to C([0,8]) âŠ‚ C([0,6]) [i] based on
    1. linear OA(128³³, 16385, F₁₂₈, 17) (dual of [16385, 16352, 18]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [i]
    2. linear OA(128²⁵, 16385, F₁₂₈, 13) (dual of [16385, 16360, 14]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,6], and minimum distance dÂ â‰¥ |{−6,−5,…,6}|+1Â =Â 14 (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 (20, 37, 2049)-net over F₁₂₈	[i]	Net Duplication
2	Digital (19, 35, 2049)-net over F₁₂₈	[i]	m-Reduction
3	(25, 42, 2049)-net in base 64	[i]	Base Change