MinT - Information on Result #3175572

Information on Result #3175572

Digital (86, 92, large)-net over F₉, using 3 times m-reduction based on digital (86, 95, large)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (21, 25, 4194301)-net over F₉, using
  - net defined by OOA [i] based on linear OOA(9²⁵, 4194301, F₉, 4, 4) (dual of [(4194301, 4), 16777179, 5]-NRT-code), using
    - appending kth column [i] based on linear OOA(9²⁵, 4194301, F₉, 3, 4) (dual of [(4194301, 3), 12582878, 5]-NRT-code), using
      - OA 2-folding and stacking [i] based on linear OA(9²⁵, 8388602, F₉, 4) (dual of [8388602, 8388577, 5]-code), using
        discarding factors / shortening the dual code based on linear OA(9²⁵, large, F₉, 4) (dual of [large, large−25, 5]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523360Â | 9⁸âˆ’1, defining interval IÂ =Â [0,3], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 5 [i]
2. digital (61, 70, 4194310)-net over F₉, using
  - (u,Â u+v)-construction [i] based on
    1. digital (0, 4, 10)-net over F₉, using
      - net from sequence [i] based on digital (0, 9)-sequence over F₉, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 0 and N(F) ≥ 10, using
        the rational function field F₉(x) [i]
        Niederreiter sequence [i]
    2. digital (57, 66, 4194300)-net over F₉, using
      - net defined by OOA [i] based on linear OOA(9⁶⁶, 4194300, F₉, 10, 9) (dual of [(4194300, 10), 41942934, 10]-NRT-code), using
        OOA 2-folding and stacking with additional row [i] based on linear OOA(9⁶⁶, 8388601, F₉, 2, 9) (dual of [(8388601, 2), 16777136, 10]-NRT-code), using
        discarding factors / shortening the dual code based on linear OOA(9⁶⁶, 8388602, F₉, 2, 9) (dual of [(8388602, 2), 16777138, 10]-NRT-code), using
        trace code [i] based on linear OOA(81³³, 4194301, F₈₁, 2, 9) (dual of [(4194301, 2), 8388569, 10]-NRT-code), using
        OOA 2-folding [i] based on linear OA(81³³, 8388602, F₈₁, 9) (dual of [8388602, 8388569, 10]-code), using
        discarding factors / shortening the dual code based on linear OA(81³³, large, F₈₁, 9) (dual of [large, large−33, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [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		This result only	Method
1	Digital (87, 92, large)-net over F₉	[i]		t-Expansion
2	Digital (88, 92, large)-net over F₉	[i]		t-Expansion