MinT - Information on Result #1214547

Information on Result #1214547

Digital (48, 60, 2818)-net over F₇, using (u,Â u+v)-construction based on

digital (3, 9, 16)-net over F₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (0, 3, 8)-net over F₇, using
    - net from sequence [i] based on digital (0, 7)-sequence over F₇, using
      - Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₇ with g(F) = 0 and N(F) ≥ 8, using
        the rational function field F₇(x) [i]
      - Niederreiter sequence [i]
  2. digital (0, 6, 8)-net over F₇, using
    - net from sequence [i] based on digital (0, 7)-sequence over F₇ (see above)
digital (39, 51, 2802)-net over F₇, using
- net defined by OOA [i] based on linear OOA(7⁵¹, 2802, F₇, 12, 12) (dual of [(2802, 12), 33573, 13]-NRT-code), using
  - OA 6-folding and stacking [i] based on linear OA(7⁵¹, 16812, F₇, 12) (dual of [16812, 16761, 13]-code), using
    - constructionÂ X applied to C_e(11) âŠ‚ C_e(10) [i] based on
      1. linear OA(7⁵¹, 16807, F₇, 12) (dual of [16807, 16756, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      2. linear OA(7⁴⁶, 16807, F₇, 11) (dual of [16807, 16761, 12]-code), using an extension C_e(10) of the primitive narrow-sense BCH-code C(I) with length 16806Â = 7⁵âˆ’1, defining interval IÂ =Â [1,10], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 11 [i]
      3. linear OA(7⁰, 5, F₇, 0) (dual of [5, 5, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(7⁰, s, F₇, 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.