MinT - Information on Result #3211570

Information on Result #3211570

Digital (161, 177, 1049603)-net over F₄, using t-expansion based on digital (160, 177, 1049603)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (24, 32, 1028)-net over F₄, using
  - trace code for nets [i] based on digital (0, 8, 257)-net over F₂₅₆, using
    - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
        the rational function field F₂₅₆(x) [i]
      - Niederreiter sequence [i]
2. digital (128, 145, 1048575)-net over F₄, using
  - net defined by OOA [i] based on linear OOA(4¹⁴⁵, 1048575, F₄, 17, 17) (dual of [(1048575, 17), 17825630, 18]-NRT-code), using
    - OOA 8-folding and stacking with additional row [i] based on linear OA(4¹⁴⁵, 8388601, F₄, 17) (dual of [8388601, 8388456, 18]-code), using
      - discarding factors / shortening the dual code based on linear OA(4¹⁴⁵, large, F₄, 17) (dual of [large, large−145, 18]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,8], and minimum distance dÂ â‰¥ |{−8,−7,…,8}|+1Â =Â 18 (BCH-bound) [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 (162, 178, 1049603)-net over F₄	[i]		Net Duplication
2	Digital (163, 179, 1049603)-net over F₄	[i]		Net Duplication