MinT - Information on Result #1843026

Information on Result #1843026

(77, 98, 53261)-net in base 27, using (u,Â u+v)-construction based on

(6, 16, 116)-net in base 27, using
- base change [i] based on digital (2, 12, 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 (61, 82, 53145)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27⁸², 53145, F₂₇, 21, 21) (dual of [(53145, 21), 1115963, 22]-NRT-code), using
  - OOA 10-folding and stacking with additional row [i] based on linear OA(27⁸², 531451, F₂₇, 21) (dual of [531451, 531369, 22]-code), using
    - constructionÂ X applied to C([0,10]) âŠ‚ C([0,9]) [i] based on
      1. linear OA(27⁸¹, 531442, F₂₇, 21) (dual of [531442, 531361, 22]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 27⁸âˆ’1, defining interval IÂ =Â [0,10], and minimum distance dÂ â‰¥ |{−10,−9,…,10}|+1Â =Â 22 (BCH-bound) [i]
      2. linear OA(27⁷³, 531442, F₂₇, 19) (dual of [531442, 531369, 20]-code), using the expurgated narrow-sense BCH-code C(I) with length 531442Â | 27⁸âˆ’1, defining interval IÂ =Â [0,9], and minimum distance dÂ â‰¥ |{−9,−8,…,9}|+1Â =Â 20 (BCH-bound) [i]
      3. linear OA(27¹, 9, F₂₇, 1) (dual of [9, 8, 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

The following results depend on this result:

	Result		This result only	Method
1	(78, 99, 53261)-net in base 27	[i]		Net Duplication