MinT - Information on Result #1208413

Information on Result #1208413

Digital (103, 120, 7389)-net over F₃, using (u,Â u+v)-construction based on

digital (1, 9, 7)-net over F₃, using
- net from sequence [i] based on digital (1, 6)-sequence over F₃, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₃ with g(F) = 1 and N(F) ≥ 7, using
    - an explicitly constructive algebraic function field [i]
digital (94, 111, 7382)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3¹¹¹, 7382, F₃, 17, 17) (dual of [(7382, 17), 125383, 18]-NRT-code), using
  - OOA 8-folding and stacking with additional row [i] based on linear OA(3¹¹¹, 59057, F₃, 17) (dual of [59057, 58946, 18]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹¹¹, 59059, F₃, 17) (dual of [59059, 58948, 18]-code), using
      - constructionÂ X applied to C_e(16) âŠ‚ C_e(15) [i] based on
        linear OA(3¹¹¹, 59049, F₃, 17) (dual of [59049, 58938, 18]-code), using an extension C_e(16) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,16], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 17 [i]
        linear OA(3¹⁰¹, 59049, F₃, 16) (dual of [59049, 58948, 17]-code), using an extension C_e(15) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,15], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 16 [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.