MinT - Information on Result #1021999

Information on Result #1021999

Linear OOA(8²⁷, 333, F₈, 3, 8) (dual of [(333, 3), 972, 9]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(8³, 73, F₈, 3, 2) (dual of [(73, 3), 216, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(8³, 73, F₈, 2, 2) (dual of [(73, 2), 143, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(8³, 73, F₈, 2) (dual of [73, 70, 3]-code), using
    - Hamming code H(3,8) [i]
linear OOA(8⁸, 130, F₈, 3, 4) (dual of [(130, 3), 382, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 8, 130)-net over F₈, using
  - trace code for nets [i] based on digital (0, 4, 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]
linear OOA(8¹⁶, 130, F₈, 3, 8) (dual of [(130, 3), 374, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 16, 130)-net over F₈, using
  - trace code for nets [i] based on digital (0, 8, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄ (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(8¹⁵⁷, 5592735, F₈, 3, 17) (dual of [(5592735, 3), 16778048, 18]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs
2	Linear OOA(8¹⁴⁹, 5592735, F₈, 3, 16) (dual of [(5592735, 3), 16778056, 17]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs