MinT - Information on Result #1022022

Information on Result #1022022

Linear OOA(9³⁰, 410, F₉, 3, 9) (dual of [(410, 3), 1200, 10]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(9⁴, 82, F₉, 3, 3) (dual of [(82, 3), 242, 4]-NRT-code), using
- appending kth column [i] based on 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]
linear OOA(9⁸, 164, F₉, 3, 4) (dual of [(164, 3), 484, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 8, 164)-net over F₉, using
  - trace code for nets [i] based on digital (0, 4, 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(9¹⁸, 164, F₉, 3, 9) (dual of [(164, 3), 474, 10]-NRT-code), using
- extracting embedded OOA [i] based on digital (9, 18, 164)-net over F₉, using
  - trace code for nets [i] based on digital (0, 9, 82)-net over F₈₁, using
    - net from sequence [i] based on digital (0, 81)-sequence over F₈₁ (see above)

Mode: Constructive and linear.

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