MinT - Information on Result #1191082

Information on Result #1191082

Digital (16, 23, 405)-net over F₈, using net defined by OOA based on linear OOA(8²³, 405, F₈, 9, 7) (dual of [(405, 9), 3622, 8]-NRT-code), using

OOA stacking with additional row [i] based on linear OOA(8²³, 406, F₈, 3, 7) (dual of [(406, 3), 1195, 8]-NRT-code), using
- generalized (u,Â u+v)-construction [i] based on
  1. linear OOA(8¹, 73, F₈, 3, 1) (dual of [(73, 3), 218, 2]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8¹, s, F₈, 3, 1) for arbitrarily large s, using
      - appending 2 arbitrary columns [i] based on linear OA(8¹, s, F₈, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
        parity-check code [i]
  2. 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]
  3. linear OOA(8⁵, 130, F₈, 3, 3) (dual of [(130, 3), 385, 4]-NRT-code), using
    - discarding factors / shortening the dual code based on linear OOA(8⁵, 207, F₈, 3, 3) (dual of [(207, 3), 616, 4]-NRT-code), using
      - OOA stacking with additional row [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]
  4. 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.

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 (115, 129, 2397147)-net over F₈	[i]		(u,Â u+v)-Construction for Nets
2	Digital (122, 137, 2397147)-net over F₈	[i]		(u,Â u+v)-Construction for Nets