MinT - Information on Result #1022023

Information on Result #1022023

Linear OOA(9²⁷, 419, F₉, 3, 8) (dual of [(419, 3), 1230, 9]-NRT-code), using generalized (u,Â u+v)-construction based on

linear OOA(9³, 91, F₉, 3, 2) (dual of [(91, 3), 270, 3]-NRT-code), using
- appending 1 arbitrary column [i] based on linear OOA(9³, 91, F₉, 2, 2) (dual of [(91, 2), 179, 3]-NRT-code), using
  - appending kth column [i] based on linear OA(9³, 91, F₉, 2) (dual of [91, 88, 3]-code), using
    - Hamming code H(3,9) [i]
linear OOA(9⁸, 164, F₉, 3, 4) (dual of [(164, 3), 484, 5]-NRT-code), using
- extracting embedded OOA [i] based on digital (4, 8, 164)-net over F₉, using
  - trace code for nets [i] based on digital (0, 4, 82)-net over F₈₁, using
    - net from sequence [i] based on digital (0, 81)-sequence over F₈₁, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 0 and N(F) ≥ 82, using
        the rational function field F₈₁(x) [i]
      - Niederreiter sequence [i]
linear OOA(9¹⁶, 164, F₉, 3, 8) (dual of [(164, 3), 476, 9]-NRT-code), using
- extracting embedded OOA [i] based on digital (8, 16, 164)-net over F₉, using
  - trace code for nets [i] based on digital (0, 8, 82)-net over F₈₁, using
    - net from sequence [i] based on digital (0, 81)-sequence over F₈₁ (see above)

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		This result only	Method
1	Linear OOA(9¹⁴⁹, 5592821, F₉, 3, 16) (dual of [(5592821, 3), 16778314, 17]-NRT-code)	[i]		(u,Â u+v)-Construction for OOAs