MinT - Information on Result #1208210

Information on Result #1208210

Digital (103, 117, 75928)-net over F₃, using (u,Â u+v)-construction based on

digital (1, 8, 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 (95, 109, 75921)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3¹⁰⁹, 75921, F₃, 14, 14) (dual of [(75921, 14), 1062785, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(3¹⁰⁹, 531447, F₃, 14) (dual of [531447, 531338, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(3¹⁰⁹, 531453, F₃, 14) (dual of [531453, 531344, 15]-code), using
      - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
        linear OA(3¹⁰⁹, 531441, F₃, 14) (dual of [531441, 531332, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(3⁹⁷, 531441, F₃, 13) (dual of [531441, 531344, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 3¹²âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(3⁰, 12, F₃, 0) (dual of [12, 12, 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.