MinT - Information on Result #1210040

Information on Result #1210040

Digital (68, 79, 52439)-net over F₄, using (u,Â u+v)-construction based on

digital (1, 6, 9)-net over F₄, using
- net from sequence [i] based on digital (1, 8)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 1 and N(F) ≥ 9, using
    - the Hermitian function field over F₄ [i]
digital (62, 73, 52430)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4⁷³, 52430, F₄, 11, 11) (dual of [(52430, 11), 576657, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(4⁷³, 262151, F₄, 11) (dual of [262151, 262078, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(4⁷³, 262153, F₄, 11) (dual of [262153, 262080, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(4⁷³, 262144, F₄, 11) (dual of [262144, 262071, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(4⁶⁴, 262144, F₄, 10) (dual of [262144, 262080, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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: 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.