MinT - Information on Result #1215898

Information on Result #1215898

Digital (123, 149, 20189)-net over F₈, using (u,Â u+v)-construction based on

digital (3, 16, 24)-net over F₈, using
- net from sequence [i] based on digital (3, 23)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 3 and N(F) ≥ 24, using
    - the Klein quartic over F₈ [i]
digital (107, 133, 20165)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8¹³³, 20165, F₈, 26, 26) (dual of [(20165, 26), 524157, 27]-NRT-code), using
  - OA 13-folding and stacking [i] based on linear OA(8¹³³, 262145, F₈, 26) (dual of [262145, 262012, 27]-code), using
    - discarding factors / shortening the dual code based on linear OA(8¹³³, 262150, F₈, 26) (dual of [262150, 262017, 27]-code), using
      - constructionÂ X applied to C_e(25) âŠ‚ C_e(24) [i] based on
        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(8¹²⁷, 262144, F₈, 25) (dual of [262144, 262017, 26]-code), using an extension C_e(24) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 8⁶âˆ’1, defining interval IÂ =Â [1,24], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 25 [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.