MinT - Information on Result #1230108

Information on Result #1230108

Digital (15, 22, 419)-net over F₉, using generalized (u,Â u+v)-construction based on

digital (1, 3, 91)-net over F₉, using
- kÂ =Â 2 construction [i]
digital (2, 5, 164)-net over F₉, using
- s-reduction based on digital (2, 5, 212)-net over F₉, using
  - net defined by OOA [i] based on linear OOA(9⁵, 212, F₉, 3, 3) (dual of [(212, 3), 631, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(9⁵, 212, F₉, 2, 3) (dual of [(212, 2), 419, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(9⁵, 212, F₉, 3) (dual of [212, 207, 4]-code or 212-cap in PG(4,9)), using
        caps completed using a computer search [i]
digital (7, 14, 164)-net over F₉, using
- trace code for nets [i] based on digital (0, 7, 82)-net over F₈₁, using
  - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
    - generalized Faure sequence [i]
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
      - the rational function field F₈₁(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 (121, 136, 2397161)-net over F₉	[i]		(u,Â u+v)-Construction for Nets
2	Digital (114, 128, 2397161)-net over F₉	[i]		(u,Â u+v)-Construction for Nets