MinT - Information on Result #1842936

Information on Result #1842936

(40, 55, 2928)-net in base 27, using (u,Â u+v)-construction based on

(5, 12, 116)-net in base 27, using
- base change [i] based on digital (2, 9, 116)-net over F₈₁, using
  - net from sequence [i] based on digital (2, 115)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 2 and N(F) ≥ 116, using
      - a function field by SÃ©mirat [i]
digital (28, 43, 2812)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27⁴³, 2812, F₂₇, 15, 15) (dual of [(2812, 15), 42137, 16]-NRT-code), using
  - OOA 7-folding and stacking with additional row [i] based on linear OA(27⁴³, 19685, F₂₇, 15) (dual of [19685, 19642, 16]-code), using
    - discarding factors / shortening the dual code based on linear OA(27⁴³, 19686, F₂₇, 15) (dual of [19686, 19643, 16]-code), using
      - constructionÂ X applied to C_e(14) âŠ‚ C_e(13) [i] based on
        linear OA(27⁴³, 19683, F₂₇, 15) (dual of [19683, 19640, 16]-code), using an extension C_e(14) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,14], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 15 [i]
        linear OA(27⁴⁰, 19683, F₂₇, 14) (dual of [19683, 19643, 15]-code), using an extension C_e(13) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,13], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 14 [i]
        linear OA(27⁰, 3, F₂₇, 0) (dual of [3, 3, 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.