MinT - Information on Result #1186796

Information on Result #1186796

Digital (169, 187, 932146)-net over F₄, using net defined by OOA based on linear OOA(4¹⁸⁷, 932146, F₄, 21, 18) (dual of [(932146, 21), 19574879, 19]-NRT-code), using

OOA 3-folding and stacking with additional row [i] based on linear OOA(4¹⁸⁷, 2796439, F₄, 3, 18) (dual of [(2796439, 3), 8389130, 19]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹⁸⁷, 2796441, F₄, 3, 18) (dual of [(2796441, 3), 8389136, 19]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(4³⁰, 240, F₄, 3, 9) (dual of [(240, 3), 690, 10]-NRT-code), using
      - extracting embedded OOA [i] based on digital (21, 30, 240)-net over F₄, using
        trace code for nets [i] based on digital (1, 10, 80)-net over F₆₄, using
        net from sequence [i] based on digital (1, 79)-sequence over F₆₄, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 1 and N(F) ≥ 80, using
        a function field by SÃ©mirat [i]
    2. linear OOA(4¹⁵⁷, 2796201, F₄, 3, 18) (dual of [(2796201, 3), 8388446, 19]-NRT-code), using
      - OOA 3-folding [i] based on linear OA(4¹⁵⁷, large, F₄, 18) (dual of [large, large−157, 19]-code), using
        the primitive expurgated narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’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.