MinT - Information on Result #1014228

Information on Result #1014228

Linear OOA(8²⁴, 468, F₈, 3, 7) (dual of [(468, 3), 1380, 8]-NRT-code), using (u,Â u+v)-construction based on

linear OOA(8⁵, 208, F₈, 3, 3) (dual of [(208, 3), 619, 4]-NRT-code), using
- appending kth column [i] based on linear OOA(8⁵, 208, F₈, 2, 3) (dual of [(208, 2), 411, 4]-NRT-code), using
  - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(8⁵, 208, F₈, 3) (dual of [208, 203, 4]-code or 208-cap in PG(4,8)), using
    - caps completed using a computer search [i]
linear OOA(8¹⁹, 260, F₈, 3, 7) (dual of [(260, 3), 761, 8]-NRT-code), using
- (u,Â u+v)-construction [i] based on
  1. linear OOA(8⁵, 208, F₈, 3, 3) (dual of [(208, 3), 619, 4]-NRT-code) (see above)
  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.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹³⁰, 5592870, F₈, 3, 14) (dual of [(5592870, 3), 16778480, 15]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(8¹³⁸, 5592870, F₈, 3, 15) (dual of [(5592870, 3), 16778472, 16]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs