MinT - Information on Result #906633

Information on Result #906633

Linear OOA(7²², 257, F₇, 2, 7) (dual of [(257, 2), 492, 8]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(7³, 57, F₇, 2, 2) (dual of [(57, 2), 111, 3]-NRT-code), using
- appending kth column [i] based on linear OA(7³, 57, F₇, 2) (dual of [57, 54, 3]-code), using
  - Hamming code H(3,7) [i]
linear OOA(7⁵, 100, F₇, 2, 3) (dual of [(100, 2), 195, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(7⁵, 132, F₇, 2, 3) (dual of [(132, 2), 259, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(7⁵, 132, F₇, 3) (dual of [132, 127, 4]-code or 132-cap in PG(4,7)), using
    - caps completed using a computer search [i]
linear OOA(7¹⁴, 100, F₇, 2, 7) (dual of [(100, 2), 186, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 14, 100)-net over F₇, using
  - trace code for nets [i] based on digital (0, 7, 50)-net over F₄₉, using
    - net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
        the rational function field F₄₉(x) [i]
      - Niederreiter sequence [i]

Mode: Constructive and linear.

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