MinT - Information on Result #1184256

Information on Result #1184256

Digital (162, 178, 1048631)-net over F₃, using net defined by OOA based on linear OOA(3¹⁷⁸, 1048631, F₃, 20, 16) (dual of [(1048631, 20), 20972442, 17]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(3¹⁷⁸, 2097263, F₃, 4, 16) (dual of [(2097263, 4), 8388874, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(3¹⁷⁸, 2097264, F₃, 4, 16) (dual of [(2097264, 4), 8388878, 17]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(3²⁷, 114, F₃, 4, 8) (dual of [(114, 4), 429, 9]-NRT-code), using
      - extracting embedded OOA [i] based on digital (19, 27, 114)-net over F₃, using
        trace code for nets [i] based on digital (1, 9, 38)-net over F₂₇, using
        net from sequence [i] based on digital (1, 37)-sequence over F₂₇, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
        a function field by SÃ©mirat [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.