MinT - Information on Result #1210273

Information on Result #1210273

Digital (76, 90, 9373)-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 (67, 81, 9363)-net over F₄, using
- net defined by OOA [i] based on linear OOA(4⁸¹, 9363, F₄, 14, 14) (dual of [(9363, 14), 131001, 15]-NRT-code), using
  - OA 7-folding and stacking [i] based on linear OA(4⁸¹, 65541, F₄, 14) (dual of [65541, 65460, 15]-code), using
    - discarding factors / shortening the dual code based on linear OA(4⁸¹, 65544, F₄, 14) (dual of [65544, 65463, 15]-code), using
      - constructionÂ X applied to C_e(13) âŠ‚ C_e(12) [i] based on
        linear OA(4⁸¹, 65536, F₄, 14) (dual of [65536, 65455, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(4⁷³, 65536, F₄, 13) (dual of [65536, 65463, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 65535Â = 4⁸âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(4⁰, 8, F₄, 0) (dual of [8, 8, 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.