MinT - Information on Result #1186590

Information on Result #1186590

Digital (146, 162, 1048587)-net over F₄, using net defined by OOA based on linear OOA(4¹⁶², 1048587, F₄, 18, 16) (dual of [(1048587, 18), 18874404, 17]-NRT-code), using

OOA 4-folding and stacking with additional row [i] based on linear OOA(4¹⁶², 4194349, F₄, 2, 16) (dual of [(4194349, 2), 8388536, 17]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(4¹⁸, 48, F₄, 2, 8) (dual of [(48, 2), 78, 9]-NRT-code), using
    - extracting embedded OOA [i] based on digital (10, 18, 48)-net over F₄, using
      - trace code for nets [i] based on digital (1, 9, 24)-net over F₁₆, using
        net from sequence [i] based on digital (1, 23)-sequence over F₁₆, using
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₁₆ with g(F) = 1 and N(F) ≥ 24, 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.