MinT - Information on Result #1211368

Information on Result #1211368

Digital (181, 209, 18742)-net over F₄, using (u,Â u+v)-construction based on

digital (5, 19, 17)-net over F₄, using
- net from sequence [i] based on digital (5, 16)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 5 and N(F) ≥ 17, using
    - an explicitly constructive algebraic function field [i]
digital (162, 190, 18725)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹⁹⁰, 18725, F₄, 28, 28) (dual of [(18725, 28), 524110, 29]-NRT-code), using
  - OA 14-folding and stacking [i] based on linear OA(4¹⁹⁰, 262150, F₄, 28) (dual of [262150, 261960, 29]-code), using
    - discarding factors / shortening the dual code based on linear OA(4¹⁹⁰, 262153, F₄, 28) (dual of [262153, 261963, 29]-code), using
      - 1 times truncation [i] based on linear OA(4¹⁹¹, 262154, F₄, 29) (dual of [262154, 261963, 30]-code), using
        constructionÂ X applied to C_e(28) âŠ‚ C_e(26) [i] based on
        linear OA(4¹⁹⁰, 262144, F₄, 29) (dual of [262144, 261954, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
        linear OA(4¹⁸¹, 262144, F₄, 27) (dual of [262144, 261963, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
        linear OA(4¹, 10, F₄, 1) (dual of [10, 9, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(4¹, s, F₄, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.