MinT - Information on Result #1184424

Information on Result #1184424

Digital (178, 195, 1048632)-net over F₃, using net defined by OOA based on linear OOA(3¹⁹⁵, 1048632, F₃, 20, 17) (dual of [(1048632, 20), 20972445, 18]-NRT-code), using

OOA 2-folding and stacking with additional row [i] based on linear OOA(3¹⁹⁵, 2097265, F₃, 4, 17) (dual of [(2097265, 4), 8388865, 18]-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(3¹⁶⁸, 2097151, F₃, 4, 17) (dual of [(2097151, 4), 8388436, 18]-NRT-code), using
    - OOA 2-folding [i] based on linear OOA(3¹⁶⁸, 4194302, F₃, 2, 17) (dual of [(4194302, 2), 8388436, 18]-NRT-code), using
      - 1 times NRT-code embedding in larger space [i] based on linear OOA(3¹⁶⁶, 4194301, F₃, 2, 17) (dual of [(4194301, 2), 8388436, 18]-NRT-code), using
        OOA 2-folding [i] based on linear OA(3¹⁶⁶, 8388602, F₃, 17) (dual of [8388602, 8388436, 18]-code), using
        discarding factors / shortening the dual code based on linear OA(3¹⁶⁶, large, F₃, 17) (dual of [large, large−166, 18]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 14348906Â = 3¹⁵âˆ’1, defining interval IÂ =Â [0,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [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.