MinT - Information on Result #1841716

Information on Result #1841716

OOA(128¹², 513, S₁₂₈, 9, 7), using OOA stacking with additional row based on OOA(128¹², 514, S₁₂₈, 3, 7), using

(u,Â u+v)-construction [i] based on
1. linear OOA(128⁴, 16385, F₁₂₈, 3, 3) (dual of [(16385, 3), 49151, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(128⁴, 16385, F₁₂₈, 2, 3) (dual of [(16385, 2), 32766, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(128⁴, 16385, F₁₂₈, 3) (dual of [16385, 16381, 4]-code or 16385-cap in PG(3,128)), using
      - ovoid in PG(3,Â 128) [i]
2. OOA(128⁸, 257, S₁₂₈, 3, 7), using
  - extracting embedded OOA [i] based on (1, 8, 257)-net in base 128, using
    - base change [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.

Results with these parameters are outside the parameter range considered by MinT and show only up in construction trees.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	(5, 12, 513)-net in base 128	[i]		Net Defined by OOA