MinT - Information on Result #1232842

Information on Result #1232842

Digital (35, 58, 228)-net over F₂₇, using generalized (u,Â u+v)-construction based on

digital (5, 12, 76)-net over F₂₇, using
- (u,Â u+v)-construction [i] based on
  1. digital (1, 4, 730)-net over F₂₇, using
    - net defined by OOA [i] based on linear OOA(27⁴, 730, F₂₇, 3, 3) (dual of [(730, 3), 2186, 4]-NRT-code), using
      - appending kth column [i] based on linear OOA(27⁴, 730, F₂₇, 2, 3) (dual of [(730, 2), 1456, 4]-NRT-code), using
        OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(27⁴, 730, F₂₇, 3) (dual of [730, 726, 4]-code or 730-cap in PG(3,27)), using
        ovoid in PG(3,Â 27) [i]
  2. digital (1, 8, 38)-net over F₂₇, using
    - net from sequence [i] based on digital (1, 37)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
        a function field by SÃ©mirat [i]
digital (6, 17, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 6 and N(F) ≥ 76, using
    - a function field by SÃ©mirat [i]
digital (6, 29, 76)-net over F₂₇, using
- net from sequence [i] based on digital (6, 75)-sequence over F₂₇ (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Digital (35, 57, 228)-net over F₂₇	[i]		m-Reduction