MinT - Information on Result #1193360

Information on Result #1193360

Digital (73, 83, 2796241)-net over F₉, using net defined by OOA based on linear OOA(9⁸³, 2796241, F₉, 15, 10) (dual of [(2796241, 15), 41943532, 11]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(9⁸³, 5592483, F₉, 3, 10) (dual of [(5592483, 3), 16777366, 11]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9⁸³, 5592484, F₉, 3, 10) (dual of [(5592484, 3), 16777369, 11]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(9⁹, 82, F₉, 3, 5) (dual of [(82, 3), 237, 6]-NRT-code), using
      - extracting embedded OOA [i] based on digital (4, 9, 82)-net over F₉, using
        base reduction for projective spaces (embedding PG(4,81) in PG(8,9)) for nets [i] based on digital (0, 5, 82)-net over F₈₁, using
        net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
        Niederreiter sequence [i]
    2. linear OOA(9⁷⁴, 5592402, F₉, 3, 10) (dual of [(5592402, 3), 16777132, 11]-NRT-code), using
      - trace code [i] based on linear OOA(81³⁷, 2796201, F₈₁, 3, 10) (dual of [(2796201, 3), 8388566, 11]-NRT-code), using
        OOA 3-folding [i] based on linear OA(81³⁷, large, F₈₁, 10) (dual of [large, large−37, 11]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 81⁴âˆ’1, defining interval IÂ =Â [0,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [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 (156, 166, 5592482)-net over F₃	[i]		Trace Code for Nets