MinT - Information on Result #1191073

Information on Result #1191073

Linear OOA(8¹⁸, 194, F₈, 9, 7) (dual of [(194, 9), 1728, 8]-NRT-code), using OOA stacking with additional row based on linear OOA(8¹⁸, 195, F₈, 3, 7) (dual of [(195, 3), 567, 8]-NRT-code), using

(u,Â u+v)-construction [i] based on
1. linear OOA(8⁴, 65, F₈, 3, 3) (dual of [(65, 3), 191, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(8⁴, 65, F₈, 2, 3) (dual of [(65, 2), 126, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁴, 65, F₈, 3) (dual of [65, 61, 4]-code or 65-cap in PG(3,8)), using
      - ovoid in PG(3,Â 8) [i]
2. linear OOA(8¹⁴, 130, F₈, 3, 7) (dual of [(130, 3), 376, 8]-NRT-code), using
  - extracting embedded OOA [i] based on digital (7, 14, 130)-net over F₈, using
    - trace code for nets [i] based on digital (0, 7, 65)-net over F₆₄, using
      - net from sequence [i] based on digital (0, 64)-sequence over F₆₄, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₆₄ with g(F) = 0 and N(F) ≥ 65, using
        the rational function field F₆₄(x) [i]
        Niederreiter sequence [i]

Mode: Constructive and linear.

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	Digital (11, 18, 194)-net over F₈	[i]		Net Defined by OOA