MinT - Information on Result #1215940

Information on Result #1215940

Digital (125, 152, 20174)-net over F₈, using (u,Â u+v)-construction based on

digital (0, 13, 9)-net over F₈, using
- net from sequence [i] based on digital (0, 8)-sequence over F₈, using
  - generalized Faure sequence [i]
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 0 and N(F) ≥ 9, using
    - the rational function field F₈(x) [i]
  - Niederreiter sequence [i]
digital (112, 139, 20165)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8¹³⁹, 20165, F₈, 27, 27) (dual of [(20165, 27), 544316, 28]-NRT-code), using
  - OOA 13-folding and stacking with additional row [i] based on linear OA(8¹³⁹, 262146, F₈, 27) (dual of [262146, 262007, 28]-code), using
    - discarding factors / shortening the dual code based on linear OA(8¹³⁹, 262150, F₈, 27) (dual of [262150, 262011, 28]-code), using
      - constructionÂ X applied to C_e(26) âŠ‚ C_e(25) [i] based on
        linear OA(8¹³⁹, 262144, F₈, 27) (dual of [262144, 262005, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
        linear OA(8¹³³, 262144, F₈, 26) (dual of [262144, 262011, 27]-code), using an extension C_e(25) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,25], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 26 [i]
        linear OA(8⁰, 6, F₈, 0) (dual of [6, 6, 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.