MinT - Information on Result #1843034

Information on Result #1843034

(61, 83, 1906)-net in base 27, using (u,Â u+v)-construction based on

(7, 18, 116)-net in base 27, using
- 2 times m-reduction [i] based on (7, 20, 116)-net in base 27, using
  - base change [i] based on digital (2, 15, 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 (43, 65, 1790)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27⁶⁵, 1790, F₂₇, 22, 22) (dual of [(1790, 22), 39315, 23]-NRT-code), using
  - OA 11-folding and stacking [i] based on linear OA(27⁶⁵, 19690, F₂₇, 22) (dual of [19690, 19625, 23]-code), using
    - constructionÂ X applied to C_e(21) âŠ‚ C_e(19) [i] based on
      1. linear OA(27⁶⁴, 19683, F₂₇, 22) (dual of [19683, 19619, 23]-code), using an extension C_e(21) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,21], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 22 [i]
      2. linear OA(27⁵⁸, 19683, F₂₇, 20) (dual of [19683, 19625, 21]-code), using an extension C_e(19) of the primitive narrow-sense BCH-code C(I) with length 19682Â = 27³âˆ’1, defining interval IÂ =Â [1,19], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 20 [i]
      3. linear OA(27¹, 7, F₂₇, 1) (dual of [7, 6, 2]-code), using
        discarding factors / shortening the dual code based on linear OA(27¹, s, F₂₇, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [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.