MinT - Information on Result #1823539

Information on Result #1823539

(17, 24, 771)-net in base 8, using base change based on digital (11, 18, 771)-net over F₁₆, using

(u,Â u+v)-construction [i] based on
1. digital (1, 4, 257)-net over F₁₆, using
  - net defined by OOA [i] based on linear OOA(16⁴, 257, F₁₆, 3, 3) (dual of [(257, 3), 767, 4]-NRT-code), using
    - appending kth column [i] based on linear OOA(16⁴, 257, F₁₆, 2, 3) (dual of [(257, 2), 510, 4]-NRT-code), using
      - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(16⁴, 257, F₁₆, 3) (dual of [257, 253, 4]-code or 257-cap in PG(3,16)), using
        ovoid in PG(3,Â 16) [i]
2. digital (7, 14, 514)-net over F₁₆, using
  - trace code for nets [i] based on digital (0, 7, 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]

Mode: Constructive.

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	(116, 130, 2397513)-net in base 8	[i]		(u,Â u+v)-Construction for Nets
2	(123, 138, 2397513)-net in base 8	[i]		(u,Â u+v)-Construction for Nets
3	OOA(8²⁴, 771, S₈, 2, 7)	[i]		Extracting Embedded OOA
4	OOA(8²⁴, 771, S₈, 3, 7)	[i]		Extracting Embedded OOA