MinT - Information on Result #1204062

Information on Result #1204062

Digital (31, 56, 1367)-net over F₁₂₈, using net defined by OOA based on linear OOA(128⁵⁶, 1367, F₁₂₈, 25, 25) (dual of [(1367, 25), 34119, 26]-NRT-code), using

OOA 12-folding and stacking with additional row [i] based on linear OA(128⁵⁶, 16405, F₁₂₈, 25) (dual of [16405, 16349, 26]-code), using
- discarding factors / shortening the dual code based on linear OA(128⁵⁶, 16408, F₁₂₈, 25) (dual of [16408, 16352, 26]-code), using
  - constructionÂ X applied to C([0,12]) âŠ‚ C([0,8]) [i] based on
    1. linear OA(128⁴⁹, 16385, F₁₂₈, 25) (dual of [16385, 16336, 26]-code), using the expurgated narrow-sense BCH-code C(I) with length 16385Â | 128⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (BCH-bound) [i]
    2. 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]
    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 (32, 56, 1367)-net over F₁₂₈	[i]	t-Expansion
2	Digital (32, 57, 1367)-net over F₁₂₈	[i]	Net Duplication
3	Digital (33, 58, 1367)-net over F₁₂₈	[i]
4	Digital (34, 59, 1367)-net over F₁₂₈	[i]
5	Digital (31, 55, 1367)-net over F₁₂₈	[i]	m-Reduction