MinT - Information on Result #1234424

Information on Result #1234424

Digital (58, 79, 26409)-net over F₆₄, using (u,Â u+v)-construction based on

digital (8, 18, 195)-net over F₆₄, using
- 1 times m-reduction [i] based on digital (8, 19, 195)-net over F₆₄, using
  - generalized (u,Â u+v)-construction [i] based on
    1. digital (0, 3, 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]
    2. digital (0, 5, 65)-net over F₆₄, using
      - net from sequence [i] based on digital (0, 64)-sequence over F₆₄ (see above)
    3. digital (0, 11, 65)-net over F₆₄, using
      - net from sequence [i] based on digital (0, 64)-sequence over F₆₄ (see above)
digital (40, 61, 26214)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64⁶¹, 26214, F₆₄, 21, 21) (dual of [(26214, 21), 550433, 22]-NRT-code), using
  - OOA 10-folding and stacking with additional row [i] based on linear OA(64⁶¹, 262141, F₆₄, 21) (dual of [262141, 262080, 22]-code), using
    - discarding factors / shortening the dual code based on linear OA(64⁶¹, 262144, F₆₄, 21) (dual of [262144, 262083, 22]-code), using
      - an extension C_e(20) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,20], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 21 [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

None.