MinT - Information on Result #1186592

Information on Result #1186592

Digital (148, 164, 1048591)-net over F₄, using net defined by OOA based on linear OOA(4¹⁶⁴, 1048591, F₄, 18, 16) (dual of [(1048591, 18), 18874474, 17]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(4¹⁶⁴, 4194365, F₄, 2, 16) (dual of [(4194365, 2), 8388566, 17]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(4¹⁶⁴, 4194367, F₄, 2, 16) (dual of [(4194367, 2), 8388570, 17]-NRT-code), using
  - (u,Â u+v)-construction [i] based on
    1. linear OOA(4²⁰, 66, F₄, 2, 8) (dual of [(66, 2), 112, 9]-NRT-code), using
      - extracting embedded OOA [i] based on digital (12, 20, 66)-net over F₄, using
        trace code for nets [i] based on digital (2, 10, 33)-net over F₁₆, using
        net from sequence [i] based on digital (2, 32)-sequence over F₁₆, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 2 and N(F) ≥ 33, using
        a function field by SÃ©mirat [i]
    2. linear OOA(4¹⁴⁴, 4194301, F₄, 2, 16) (dual of [(4194301, 2), 8388458, 17]-NRT-code), using
      - OOA 2-folding [i] based on linear OA(4¹⁴⁴, 8388602, F₄, 16) (dual of [8388602, 8388458, 17]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹⁴⁴, large, F₄, 16) (dual of [large, large−144, 17]-code), using
        the primitive narrow-sense BCH-code C(I) with length 16777215Â = 4¹²âˆ’1, defining interval IÂ =Â [1,16], 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.