MinT - Information on Result #1230560

Information on Result #1230560

Digital (26, 37, 1542)-net over F₁₆, using generalized (u,Â u+v)-construction based on

digital (2, 5, 514)-net over F₁₆, using
- s-reduction based on digital (2, 5, 629)-net over F₁₆, using
  - net defined by OOA [i] based on linear OOA(16⁵, 629, F₁₆, 3, 3) (dual of [(629, 3), 1882, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(16⁵, 629, F₁₆, 2, 3) (dual of [(629, 2), 1253, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(16⁵, 629, F₁₆, 3) (dual of [629, 624, 4]-code or 629-cap in PG(4,16)), using
        caps completed using a computer search [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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Digital (27, 38, 1542)-net over F₁₆	[i]		Net Duplication
2	Digital (26, 36, 1542)-net over F₁₆	[i]		m-Reduction