MinT - Information on Result #1013692

Information on Result #1013692

Linear OOA(7¹⁸, 150, F₇, 3, 7) (dual of [(150, 3), 432, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(7⁴, 50, F₇, 3, 3) (dual of [(50, 3), 146, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(7⁴, 50, F₇, 2, 3) (dual of [(50, 2), 96, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(7⁴, 50, F₇, 3) (dual of [50, 46, 4]-code or 50-cap in PG(3,7)), using
    - ovoid in PG(3,Â 7) [i]
linear OOA(7¹⁴, 100, F₇, 3, 7) (dual of [(100, 3), 286, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 14, 100)-net over F₇, using
  - trace code for nets [i] based on digital (0, 7, 50)-net over F₄₉, using
    - net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
        the rational function field F₄₉(x) [i]
      - Niederreiter sequence [i]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(7¹⁸, 149, F₇, 9, 7) (dual of [(149, 9), 1323, 8]-NRT-code)	[i]		OOA Stacking with Additional Row