MinT - Information on Result #1208357

Information on Result #1208357

Digital (234, 249, 4793568)-net over F₃, using (u,Â u+v)-construction based on

digital (14, 21, 84)-net over F₃, using
- trace code for nets [i] based on digital (0, 7, 28)-net over F₂₇, using
  - net from sequence [i] based on digital (0, 27)-sequence over F₂₇, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 0 and N(F) ≥ 28, using
      - the rational function field F₂₇(x) [i]
    - Niederreiter sequence [i]
digital (213, 228, 4793484)-net over F₃, using
- trace code for nets [i] based on digital (42, 57, 1198371)-net over F₈₁, using
  - net defined by OOA [i] based on linear OOA(81⁵⁷, 1198371, F₈₁, 15, 15) (dual of [(1198371, 15), 17975508, 16]-NRT-code), using
    - OOA 7-folding and stacking with additional row [i] based on linear OA(81⁵⁷, 8388598, F₈₁, 15) (dual of [8388598, 8388541, 16]-code), using
      - discarding factors / shortening the dual code based on linear OA(81⁵⁷, large, F₈₁, 15) (dual of [large, large−57, 16]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (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 (235, 250, 4793568)-net over F₃	[i]		Net Duplication
2	Linear OOA(3²⁴⁹, 4793568, F₃, 5, 15) (dual of [(4793568, 5), 23967591, 16]-NRT-code)	[i]		Extracting Embedded OOA