MinT - Information on Result #1193106

Information on Result #1193106

Digital (15, 22, 418)-net over F₉, using net defined by OOA based on linear OOA(9²², 418, F₉, 9, 7) (dual of [(418, 9), 3740, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(9²², 419, F₉, 3, 7) (dual of [(419, 3), 1235, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. 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]
  2. 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]
  3. 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.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t, t and s.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		This result only	Method
1	Digital (114, 128, 2397160)-net over F₉	[i]		(u,Â u+v)-Construction for Nets
2	Digital (121, 136, 2397160)-net over F₉	[i]		(u,Â u+v)-Construction for Nets