MinT - Information on Result #1216020

Information on Result #1216020

Digital (117, 146, 2369)-net over F₈, using (u,Â u+v)-construction based on

digital (5, 19, 28)-net over F₈, using
- net from sequence [i] based on digital (5, 27)-sequence over F₈, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈ with g(F) = 5 and N(F) ≥ 28, using
    - a function field by SÃ©mirat [i]
digital (98, 127, 2341)-net over F₈, using
- net defined by OOA [i] based on linear OOA(8¹²⁷, 2341, F₈, 29, 29) (dual of [(2341, 29), 67762, 30]-NRT-code), using
  - OOA 14-folding and stacking with additional row [i] based on linear OA(8¹²⁷, 32775, F₈, 29) (dual of [32775, 32648, 30]-code), using
    - discarding factors / shortening the dual code based on linear OA(8¹²⁷, 32779, F₈, 29) (dual of [32779, 32652, 30]-code), using
      - constructionÂ X applied to C_e(28) âŠ‚ C_e(26) [i] based on
        linear OA(8¹²⁶, 32768, F₈, 29) (dual of [32768, 32642, 30]-code), using an extension C_e(28) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,28], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 29 [i]
        linear OA(8¹¹⁶, 32768, F₈, 27) (dual of [32768, 32652, 28]-code), using an extension C_e(26) of the primitive narrow-sense BCH-code C(I) with length 32767Â = 8⁵âˆ’1, defining interval IÂ =Â [1,26], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 27 [i]
        linear OA(8¹, 11, F₈, 1) (dual of [11, 10, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.