MinT - Information on Result #1207954

Information on Result #1207954

Digital (66, 77, 11818)-net over F₃, using (u,Â u+v)-construction based on

digital (1, 6, 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 (60, 71, 11811)-net over F₃, using
- net defined by OOA [i] based on linear OOA(3⁷¹, 11811, F₃, 11, 11) (dual of [(11811, 11), 129850, 12]-NRT-code), using
  - OOA 5-folding and stacking with additional row [i] based on linear OA(3⁷¹, 59056, F₃, 11) (dual of [59056, 58985, 12]-code), using
    - discarding factors / shortening the dual code based on linear OA(3⁷¹, 59059, F₃, 11) (dual of [59059, 58988, 12]-code), using
      - constructionÂ X applied to C_e(10) âŠ‚ C_e(9) [i] based on
        linear OA(3⁷¹, 59049, F₃, 11) (dual of [59049, 58978, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
        linear OA(3⁶¹, 59049, F₃, 10) (dual of [59049, 58988, 11]-code), using an extension C_e(9) of the primitive narrow-sense BCH-code C(I) with length 59048Â = 3¹⁰âˆ’1, defining interval IÂ =Â [1,9], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 10 [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.