MinT - Information on Result #1843044

Information on Result #1843044

(61, 84, 1890)-net in base 27, using (u,Â u+v)-construction based on

(5, 16, 100)-net in base 27, using
- base change [i] based on digital (1, 12, 100)-net over F₈₁, using
  - net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
      - a function field by SÃ©mirat [i]
digital (45, 68, 1790)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27⁶⁸, 1790, F₂₇, 23, 23) (dual of [(1790, 23), 41102, 24]-NRT-code), using
  - OOA 11-folding and stacking with additional row [i] based on linear OA(27⁶⁸, 19691, F₂₇, 23) (dual of [19691, 19623, 24]-code), using
    - constructionÂ X applied to C([0,11]) âŠ‚ C([0,10]) [i] based on
      1. linear OA(27⁶⁷, 19684, F₂₇, 23) (dual of [19684, 19617, 24]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 27⁶âˆ’1, defining interval IÂ =Â [0,11], and minimum distance dÂ â‰¥ |{−11,−10,…,11}|+1Â =Â 24 (BCH-bound) [i]
      2. linear OA(27⁶¹, 19684, F₂₇, 21) (dual of [19684, 19623, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 19684Â | 27⁶âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [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.