MinT - Information on Result #1215272

Information on Result #1215272

Digital (75, 88, 349551)-net over F₈, using (u,Â u+v)-construction based on

digital (4, 10, 25)-net over F₈, using
- net from sequence [i] based on digital (4, 24)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 4 and N(F) ≥ 25, using
    - a function field by SÃ©mirat [i]
digital (65, 78, 349526)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8⁷⁸, 349526, F₈, 13, 13) (dual of [(349526, 13), 4543760, 14]-NRT-code), using
  - OOA 6-folding and stacking with additional row [i] based on linear OA(8⁷⁸, 2097157, F₈, 13) (dual of [2097157, 2097079, 14]-code), using
    - discarding factors / shortening the dual code based on linear OA(8⁷⁸, 2097159, F₈, 13) (dual of [2097159, 2097081, 14]-code), using
      - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
        linear OA(8⁷⁸, 2097152, F₈, 13) (dual of [2097152, 2097074, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
        linear OA(8⁷¹, 2097152, F₈, 12) (dual of [2097152, 2097081, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 2097151Â = 8⁷âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
        linear OA(8⁰, 7, F₈, 0) (dual of [7, 7, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(8⁰, s, F₈, 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.