MinT - Information on Result #1192146

Information on Result #1192146

Digital (138, 156, 1864177)-net over F₈, using net defined by OOA based on linear OOA(8¹⁵⁶, 1864177, F₈, 21, 18) (dual of [(1864177, 21), 39147561, 19]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(8¹⁵⁶, 5592532, F₈, 3, 18) (dual of [(5592532, 3), 16777440, 19]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8¹⁸, 130, F₈, 3, 9) (dual of [(130, 3), 372, 10]-NRT-code), using
    - extracting embedded OOA [i] based on digital (9, 18, 130)-net over F₈, using
      - trace code for nets [i] based on digital (0, 9, 65)-net over F₆₄, using
        net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
        Niederreiter sequence [i]
  2. linear OOA(8¹³⁸, 5592402, F₈, 3, 18) (dual of [(5592402, 3), 16777068, 19]-NRT-code), using
    - trace code [i] based on linear OOA(64⁶⁹, 2796201, F₆₄, 3, 18) (dual of [(2796201, 3), 8388534, 19]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(64⁶⁹, large, F₆₄, 18) (dual of [large, large−69, 19]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 64⁴âˆ’1, defining interval IÂ =Â [0,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 19 [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.