MinT - Information on Result #1779970

Information on Result #1779970

Digital (171, 201, 99677)-net over F₄, using embedding of OOA with Gilbertâ€“VarÅ¡amov bound based on linear OOA(4²⁰¹, 99677, F₄, 2, 30) (dual of [(99677, 2), 199153, 31]-NRT-code), using

discarding factors / shortening the dual code based on linear OOA(4²⁰¹, 131077, F₄, 2, 30) (dual of [(131077, 2), 261953, 31]-NRT-code), using
- 4¹ times duplication [i] based on linear OOA(4²⁰⁰, 131077, F₄, 2, 30) (dual of [(131077, 2), 261954, 31]-NRT-code), using
  - OOA 2-folding [i] based on linear OA(4²⁰⁰, 262154, F₄, 30) (dual of [262154, 261954, 31]-code), using
    - 1 times code embedding in larger space [i] based on linear OA(4¹⁹⁹, 262153, F₄, 30) (dual of [262153, 261954, 31]-code), using
      - constructionÂ X applied to C_e(29) âŠ‚ C_e(28) [i] based on
        linear OA(4¹⁹⁹, 262144, F₄, 30) (dual of [262144, 261945, 31]-code), using an extension C_e(29) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,29], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 30 [i]
        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(4⁰, 9, F₄, 0) (dual of [9, 9, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(4⁰, s, F₄, 0) (dual of [s, s, 1]-code) for arbitrarily large s, using
        OA with only one run / dual of code without redundancy [i]

Mode: 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.