MinT - Information on Result #1215048

Information on Result #1215048

Digital (58, 66, 4194430)-net over F₈, using (u,Â u+v)-construction based on

digital (4, 8, 130)-net over F₈, using
- trace code for nets [i] based on digital (0, 4, 65)-net over F₆₄, using
  - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
      - the rational function field F₆₄(x) [i]
    - Niederreiter sequence [i]
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 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		This result only	Method
1	Digital (59, 67, 4194430)-net over F₈	[i]		Net Duplication