MinT - Information on Result #896483

Information on Result #896483

Linear OOA(8²³, 390, F₈, 2, 7) (dual of [(390, 2), 757, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁵, 208, F₈, 2, 3) (dual of [(208, 2), 411, 4]-NRT-code), using
- OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁵, 208, F₈, 3) (dual of [208, 203, 4]-code or 208-cap in PG(4,8)), using
  - caps completed using a computer search [i]
linear OOA(8¹⁸, 195, F₈, 2, 7) (dual of [(195, 2), 372, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁴, 65, F₈, 2, 3) (dual of [(65, 2), 126, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁴, 65, F₈, 3) (dual of [65, 61, 4]-code or 65-cap in PG(3,8)), using
      - ovoid in PG(3,Â 8) [i]
  2. linear OOA(8¹⁴, 130, F₈, 2, 7) (dual of [(130, 2), 246, 8]-NRT-code), using
    - extracting embedded OOA [i] based on digital (7, 14, 130)-net over F₈, using
      - trace code for nets [i] based on digital (0, 7, 65)-net over F₆₄, using
        net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
        Niederreiter sequence [i]

Mode: Constructive and linear.

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