MinT - Information on Result #1230277

Information on Result #1230277

Digital (28, 39, 1542)-net over F₁₆, using generalized (u,Â u+v)-construction based on

digital (1, 3, 257)-net over F₁₆, using
- s-reduction based on digital (1, 3, 273)-net over F₁₆, using
  - kÂ =Â 2 construction [i]
digital (1, 4, 257)-net over F₁₆, using
- net defined by OOA [i] based on linear OOA(16⁴, 257, F₁₆, 3, 3) (dual of [(257, 3), 767, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(16⁴, 257, F₁₆, 2, 3) (dual of [(257, 2), 510, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(16⁴, 257, F₁₆, 3) (dual of [257, 253, 4]-code or 257-cap in PG(3,16)), using
      - ovoid in PG(3,Â 16) [i]
digital (5, 10, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 5, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅₆ with g(F) = 0 and N(F) ≥ 257, using
      - the rational function field F₂₅₆(x) [i]
    - Niederreiter sequence [i]
digital (11, 22, 514)-net over F₁₆, using
- trace code for nets [i] based on digital (0, 11, 257)-net over F₂₅₆, using
  - net from sequence [i] based on digital (0, 256)-sequence over F₂₅₆ (see above)

Mode: Constructive and linear.

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