MinT - Information on Result #1211064

Information on Result #1211064

Digital (142, 165, 23837)-net over F₄, using (u,Â u+v)-construction based on

digital (0, 11, 5)-net over F₄, using
- net from sequence [i] based on digital (0, 4)-sequence over F₄, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 0 and N(F) ≥ 5, using
    - the rational function field F₄(x) [i]
  - Niederreiter sequence [i]
digital (131, 154, 23832)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4¹⁵⁴, 23832, F₄, 23, 23) (dual of [(23832, 23), 547982, 24]-NRT-code), using
  - OOA 11-folding and stacking with additional row [i] based on linear OA(4¹⁵⁴, 262153, F₄, 23) (dual of [262153, 261999, 24]-code), using
    - constructionÂ X applied to C_e(22) âŠ‚ C_e(21) [i] based on
      1. linear OA(4¹⁵⁴, 262144, F₄, 23) (dual of [262144, 261990, 24]-code), using an extension C_e(22) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,22], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 23 [i]
      2. linear OA(4¹⁴⁵, 262144, F₄, 22) (dual of [262144, 261999, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      3. 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.