MinT - Information on Result #897504

Information on Result #897504

Linear OOA(9⁵², 464, F₉, 2, 15) (dual of [(464, 2), 876, 16]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(9¹⁸, 246, F₉, 2, 7) (dual of [(246, 2), 474, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(9⁴, 82, F₉, 2, 3) (dual of [(82, 2), 160, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(9⁴, 82, F₉, 3) (dual of [82, 78, 4]-code or 82-cap in PG(3,9)), using
      - ovoid in PG(3,Â 9) [i]
  2. linear OOA(9¹⁴, 164, F₉, 2, 7) (dual of [(164, 2), 314, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 14, 164)-net over F₉, using
      - trace code for nets [i] based on digital (0, 7, 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]
linear OOA(9³⁴, 232, F₉, 2, 15) (dual of [(232, 2), 430, 16]-NRT-code), using
- extracting embedded OOA [i] based on digital (19, 34, 232)-net over F₉, using
  - trace code for nets [i] based on digital (2, 17, 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]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.

Other Results with Identical Parameters

None.

Depending Results

None.