MinT - Information on Result #1215064

Information on Result #1215064

Digital (79, 87, large)-net over F₈, using (u,Â u+v)-construction based on

digital (21, 25, 4194301)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8²⁵, 4194301, F₈, 4, 4) (dual of [(4194301, 4), 16777179, 5]-NRT-code), using
  - appending kth column [i] based on linear OOA(8²⁵, 4194301, F₈, 3, 4) (dual of [(4194301, 3), 12582878, 5]-NRT-code), using
    - OA 2-folding and stacking [i] based on linear OA(8²⁵, 8388602, F₈, 4) (dual of [8388602, 8388577, 5]-code), using
      - discarding factors / shortening the dual code based on linear OA(8²⁵, large, F₈, 4) (dual of [large, large−25, 5]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 8⁸âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
digital (54, 62, 4194309)-net over F₈, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 4, 9)-net over F₈, using
    - net from sequence [i] based on digital (0, 8)-sequence over F₈, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 0 and N(F) ≥ 9, using
        the rational function field F₈(x) [i]
      - Niederreiter sequence [i]
  2. digital (50, 58, 4194300)-net over F₈, using
    - net defined by OOA [i] based on linear OOA(8⁵⁸, 4194300, F₈, 10, 8) (dual of [(4194300, 10), 41942942, 9]-NRT-code), using
      - OOA 2-folding and stacking with additional row [i] based on linear OOA(8⁵⁸, 8388601, F₈, 2, 8) (dual of [(8388601, 2), 16777144, 9]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(8⁵⁸, 8388602, F₈, 2, 8) (dual of [(8388602, 2), 16777146, 9]-NRT-code), using
        trace code [i] based on linear OOA(64²⁹, 4194301, F₆₄, 2, 8) (dual of [(4194301, 2), 8388573, 9]-NRT-code), using
        OOA 2-folding [i] based on linear OA(64²⁹, 8388602, F₆₄, 8) (dual of [8388602, 8388573, 9]-code), using
        discarding factors / shortening the dual code based on linear OA(64²⁹, large, F₆₄, 8) (dual of [large, large−29, 9]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,7], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 9 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and t, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Digital (80, 87, large)-net over F₈	[i]	t-Expansion
2	Digital (81, 87, large)-net over F₈	[i]
3	Digital (82, 87, large)-net over F₈	[i]
4	Digital (83, 87, large)-net over F₈	[i]
5	Digital (84, 87, large)-net over F₈	[i]
6	Digital (80, 88, large)-net over F₈	[i]	Net Duplication
7	Digital (81, 89, large)-net over F₈	[i]
8	Digital (82, 90, large)-net over F₈	[i]
9	Digital (83, 91, large)-net over F₈	[i]
10	Digital (84, 92, large)-net over F₈	[i]
11	Digital (79, 86, large)-net over F₈	[i]	m-Reduction
12	Digital (79, 85, large)-net over F₈	[i]
13	Digital (79, 84, large)-net over F₈	[i]
14	Digital (79, 83, large)-net over F₈	[i]
15	Digital (79, 82, large)-net over F₈	[i]