MinT - Information on Result #1210275

Information on Result #1210275

Digital (86, 100, 37460)-net over F₄, using (u,Â u+v)-construction based on

digital (2, 9, 10)-net over F₄, using
- net from sequence [i] based on digital (2, 9)-sequence over F₄, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄ with g(F) = 2 and N(F) ≥ 10, using
    - an explicitly constructive algebraic function field [i]
digital (77, 91, 37450)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4⁹¹, 37450, F₄, 14, 14) (dual of [(37450, 14), 524209, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(4⁹¹, 262150, F₄, 14) (dual of [262150, 262059, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(4⁹¹, 262153, F₄, 14) (dual of [262153, 262062, 15]-code), using
      - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
        linear OA(4⁹¹, 262144, F₄, 14) (dual of [262144, 262053, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(4⁸², 262144, F₄, 13) (dual of [262144, 262062, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 4⁹âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        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.