MinT - Information on Result #1842914

Information on Result #1842914

(44, 57, 88656)-net in base 27, using (u,Â u+v)-construction based on

(2, 8, 82)-net in base 27, using
- base change [i] based on digital (0, 6, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(x) [i]
    - Niederreiter sequence [i]
digital (36, 49, 88574)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27⁴⁹, 88574, F₂₇, 13, 13) (dual of [(88574, 13), 1151413, 14]-NRT-code), using
  - OOA 6-folding and stacking with additional row [i] based on linear OA(27⁴⁹, 531445, F₂₇, 13) (dual of [531445, 531396, 14]-code), using
    - constructionÂ X applied to C_e(12) âŠ‚ C_e(11) [i] based on
      1. linear OA(27⁴⁹, 531441, F₂₇, 13) (dual of [531441, 531392, 14]-code), using an extension C_e(12) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]
      2. linear OA(27⁴⁵, 531441, F₂₇, 12) (dual of [531441, 531396, 13]-code), using an extension C_e(11) of the primitive narrow-sense BCH-code C(I) with length 531440Â = 27⁴âˆ’1, defining interval IÂ =Â [1,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 12 [i]
      3. linear OA(27⁰, 4, F₂₇, 0) (dual of [4, 4, 1]-code), using
        discarding factors / shortening the dual code based on linear OA(27⁰, s, F₂₇, 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.

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.