MinT - Information on Result #3221034

Information on Result #3221034

Digital (229, 253, 699245)-net over F₄, using t-expansion based on digital (228, 253, 699245)-net over F₄, using

(u,Â u+v)-construction [i] based on
1. digital (24, 36, 195)-net over F₄, using
  - trace code for nets [i] based on digital (0, 12, 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]
2. digital (192, 217, 699050)-net over F₄, using
  - net defined by OOA [i] based on linear OOA(4²¹⁷, 699050, F₄, 25, 25) (dual of [(699050, 25), 17476033, 26]-NRT-code), using
    - OOA 12-folding and stacking with additional row [i] based on linear OA(4²¹⁷, 8388601, F₄, 25) (dual of [8388601, 8388384, 26]-code), using
      - discarding factors / shortening the dual code based on linear OA(4²¹⁷, large, F₄, 25) (dual of [large, large−217, 26]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 16777217Â | 4²⁴âˆ’1, defining interval IÂ =Â [0,12], and minimum distance dÂ â‰¥ |{−12,−11,…,12}|+1Â =Â 26 (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 (230, 254, 699245)-net over F₄	[i]		Net Duplication