MinT - Information on Result #1234938

Information on Result #1234938

Linear OOA(3¹²⁷, 6291454, F₃, 4, 9) (dual of [(6291454, 4), 25165689, 10]-NRT-code), using extracting embedded OOA based on digital (118, 127, 6291454)-net over F₃, using

(u,Â u+v)-construction [i] based on
1. digital (0, 4, 4)-net over F₃, using
  - net from sequence [i] based on digital (0, 3)-sequence over F₃, using
    - Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 0 and N(F) ≥ 4, using
      - the rational function field F₃(x) [i]
    - Niederreiter sequence [i]
2. digital (114, 123, 6291450)-net over F₃, using
  - trace code for nets [i] based on digital (32, 41, 2097150)-net over F₂₇, using
    - net defined by OOA [i] based on linear OOA(27⁴¹, 2097150, F₂₇, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-code), using
      - OOA 4-folding and stacking with additional row [i] based on linear OA(27⁴¹, 8388601, F₂₇, 9) (dual of [8388601, 8388560, 10]-code), using
        discarding factors / shortening the dual code based on linear OA(27⁴¹, large, F₂₇, 9) (dual of [large, large−41, 10]-code), using
        the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’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 s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(3¹²⁷, 6291453, F₃, 5, 9) (dual of [(6291453, 5), 31457138, 10]-NRT-code)	[i]		OOA Stacking with Additional Row