MinT - Information on Result #1838560

Information on Result #1838560

OOA(128¹², 514, S₁₂₈, 4, 7), using (u,Â u+v)-construction based on

linear OOA(128⁴, 16385, F₁₂₈, 4, 3) (dual of [(16385, 4), 65536, 4]-NRT-code), using
- appending 1 arbitrary column [i] based on 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]
OOA(128⁸, 257, S₁₂₈, 4, 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]

None.

The following results depend on this result:

	Result		This result only	Method
1	OOA(128⁵⁸, 2097664, S₁₂₈, 4, 14)	[i]		(u,Â u+v)-Construction for OOAs
2	OOA(128⁶², 2097664, S₁₂₈, 4, 15)	[i]		(u,Â u+v)-Construction for OOAs