MinT - Information on Result #1184246

Information on Result #1184246

Digital (155, 171, 1048594)-net over F₃, using net defined by OOA based on linear OOA(3¹⁷¹, 1048594, F₃, 20, 16) (dual of [(1048594, 20), 20971709, 17]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(3¹⁷¹, 2097189, F₃, 4, 16) (dual of [(2097189, 4), 8388585, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁷¹, 2097190, F₃, 4, 16) (dual of [(2097190, 4), 8388589, 17]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(3²⁰, 40, F₃, 4, 8) (dual of [(40, 4), 140, 9]-NRT-code), using
      - extracting embedded OOA [i] based on digital (12, 20, 40)-net over F₃, using
        trace code for nets [i] based on digital (2, 10, 20)-net over F₉, using
        net from sequence [i] based on digital (2, 19)-sequence over F₉, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 2 and N(F) ≥ 20, using
        a function field by GarcÃa and Quoos [i]
    2. linear OOA(3¹⁵¹, 2097150, F₃, 4, 16) (dual of [(2097150, 4), 8388449, 17]-NRT-code), using
      - OOA 4-folding [i] based on linear OA(3¹⁵¹, 8388600, F₃, 16) (dual of [8388600, 8388449, 17]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹⁵¹, large, F₃, 16) (dual of [large, large−151, 17]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [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

None.