MinT - Information on Result #1229723

Information on Result #1229723

Digital (13, 19, 208)-net over F₇, using generalized (u,Â u+v)-construction based on

digital (0, 2, 8)-net over F₇, using
- kÂ =Â 2 construction [i]
digital (2, 5, 100)-net over F₇, using
- s-reduction based on digital (2, 5, 132)-net over F₇, using
  - net defined by OOA [i] based on linear OOA(7⁵, 132, F₇, 3, 3) (dual of [(132, 3), 391, 4]-NRT-code), using
    - appending kth column [i] 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]
digital (6, 12, 100)-net over F₇, using
- trace code for nets [i] based on digital (0, 6, 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.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (97, 109, 1921809)-net over F₇	[i]		(u,Â u+v)-Construction for Nets