MinT - Information on Result #1022025

Information on Result #1022025

Linear OOA(9²², 419, F₉, 3, 7) (dual of [(419, 3), 1235, 8]-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(9⁵, 164, F₉, 3, 3) (dual of [(164, 3), 487, 4]-NRT-code), using
- discarding factors / shortening the dual code based on linear OOA(9⁵, 211, F₉, 3, 3) (dual of [(211, 3), 628, 4]-NRT-code), using
  - OOA stacking with additional row [i] based on linear OA(9⁵, 212, F₉, 3) (dual of [212, 207, 4]-code or 212-cap in PG(4,9)), using
    - caps completed using a computer search [i]
linear OOA(9¹⁴, 164, F₉, 3, 7) (dual of [(164, 3), 478, 8]-NRT-code), using
- extracting embedded OOA [i] based on digital (7, 14, 164)-net over F₉, using
  - trace code for nets [i] based on digital (0, 7, 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]

Mode: Constructive and linear.

None.

The following results depend on this result:

	Result		Method
1	Linear OOA(9¹³⁶, 5592821, F₉, 3, 15) (dual of [(5592821, 3), 16778327, 16]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(9¹²⁸, 5592821, F₉, 3, 14) (dual of [(5592821, 3), 16778335, 15]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
3	Linear OOA(9²², 418, F₉, 9, 7) (dual of [(418, 9), 3740, 8]-NRT-code)	[i]	OOA Stacking with Additional Row