MinT - Information on Result #1229940

Information on Result #1229940

Digital (16, 23, 406)-net over F₈, using generalized (u,Â u+v)-construction based on

digital (0, 1, 73)-net over F₈, using
- s-reduction based on digital (0, 1, s)-net over F₈ for arbitrarily large s, using
  - construction for strength kÂ =Â 1 [i]
digital (1, 3, 73)-net over F₈, using
- kÂ =Â 2 construction [i]
digital (2, 5, 130)-net over F₈, using
- s-reduction based on digital (2, 5, 208)-net over F₈, using
  - net defined by OOA [i] based on linear OOA(8⁵, 208, F₈, 3, 3) (dual of [(208, 3), 619, 4]-NRT-code), using
    - appending kth column [i] 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]
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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Digital (122, 137, 2397148)-net over F₈	[i]		(u,Â u+v)-Construction for Nets
2	Digital (115, 129, 2397148)-net over F₈	[i]		(u,Â u+v)-Construction for Nets