MinT - Information on Result #1234428

Information on Result #1234428

Digital (50, 68, 29322)-net over F₆₄, using (u,Â u+v)-construction based on

digital (7, 16, 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, 4, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄ (see above)
  3. digital (0, 9, 65)-net over F₆₄, using
    - net from sequence [i] based on digital (0, 64)-sequence over F₆₄ (see above)
digital (34, 52, 29127)-net over F₆₄, using
- net defined by OOA [i] based on linear OOA(64⁵², 29127, F₆₄, 18, 18) (dual of [(29127, 18), 524234, 19]-NRT-code), using
  - OA 9-folding and stacking [i] based on linear OA(64⁵², 262143, F₆₄, 18) (dual of [262143, 262091, 19]-code), using
    - discarding factors / shortening the dual code based on linear OA(64⁵², 262144, F₆₄, 18) (dual of [262144, 262092, 19]-code), using
      - an extension C_e(17) of the primitive narrow-sense BCH-code C(I) with length 262143Â = 64³âˆ’1, defining interval IÂ =Â [1,17], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 18 [i]

Mode: Constructive and linear.

None.

None.