MinT - Information on Result #1208911

Information on Result #1208911

Digital (197, 229, 3699)-net over F₃, using (u,Â u+v)-construction based on

digital (2, 18, 8)-net over F₃, using
- net from sequence [i] based on digital (2, 7)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 2 and N(F) ≥ 8, using
    - an explicitly constructive algebraic function field [i]
digital (179, 211, 3691)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3²¹¹, 3691, F₃, 32, 32) (dual of [(3691, 32), 117901, 33]-NRT-code), using
  - OA 16-folding and stacking [i] based on linear OA(3²¹¹, 59056, F₃, 32) (dual of [59056, 58845, 33]-code), using
    - discarding factors / shortening the dual code based on linear OA(3²¹¹, 59059, F₃, 32) (dual of [59059, 58848, 33]-code), using
      - constructionÂ X applied to C_e(31) âŠ‚ C_e(30) [i] based on
        linear OA(3²¹¹, 59049, F₃, 32) (dual of [59049, 58838, 33]-code), using an extension C_e(31) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,31], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 32 [i]
        linear OA(3²⁰¹, 59049, F₃, 31) (dual of [59049, 58848, 32]-code), using an extension C_e(30) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,30], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 31 [i]
        linear OA(3⁰, 10, F₃, 0) (dual of [10, 10, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(3⁰, s, F₃, 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.