MinT - Information on Result #1232977

Information on Result #1232977

Digital (41, 50, 2097916)-net over F₂₇, using (u,Â u+v)-construction based on

digital (5, 9, 766)-net over F₂₇, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 0, 28)-net over F₂₇, using
    - s-reduction based on digital (0, 0, s)-net over F₂₇ for arbitrarily large s, using
      - arbitrary set of 27⁰ points [i]
  2. digital (0, 0, 28)-net over F₂₇ (see above)
  3. digital (0, 0, 28)-net over F₂₇ (see above)
  4. digital (0, 0, 28)-net over F₂₇ (see above)
  5. digital (0, 0, 28)-net over F₂₇ (see above)
  6. digital (0, 0, 28)-net over F₂₇ (see above)
  7. digital (0, 0, 28)-net over F₂₇ (see above)
  8. digital (0, 0, 28)-net over F₂₇ (see above)
  9. digital (0, 0, 28)-net over F₂₇ (see above)
  10. digital (0, 0, 28)-net over F₂₇ (see above)
  11. digital (0, 0, 28)-net over F₂₇ (see above)
  12. digital (0, 0, 28)-net over F₂₇ (see above)
  13. digital (0, 0, 28)-net over F₂₇ (see above)
  14. digital (0, 0, 28)-net over F₂₇ (see above)
  15. digital (0, 0, 28)-net over F₂₇ (see above)
  16. digital (0, 0, 28)-net over F₂₇ (see above)
  17. digital (0, 0, 28)-net over F₂₇ (see above)
  18. digital (0, 0, 28)-net over F₂₇ (see above)
  19. digital (0, 0, 28)-net over F₂₇ (see above)
  20. digital (0, 0, 28)-net over F₂₇ (see above)
  21. digital (0, 0, 28)-net over F₂₇ (see above)
  22. digital (0, 0, 28)-net over F₂₇ (see above)
  23. digital (0, 0, 28)-net over F₂₇ (see above)
  24. digital (0, 1, 28)-net over F₂₇, using
    - s-reduction based on digital (0, 1, s)-net over F₂₇ for arbitrarily large s, using
      - construction for strength kÂ =Â 1 [i]
  25. digital (0, 1, 28)-net over F₂₇ (see above)
  26. digital (0, 2, 28)-net over F₂₇, using
    - kÂ =Â 2 construction [i]
  27. digital (1, 5, 38)-net over F₂₇, using
    - net from sequence [i] based on digital (1, 37)-sequence over F₂₇, using
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 1 and N(F) ≥ 38, using
        a function field by SÃ©mirat [i]
digital (32, 41, 2097150)-net over F₂₇, using
- net defined by OOA [i] based on linear OOA(27⁴¹, 2097150, F₂₇, 9, 9) (dual of [(2097150, 9), 18874309, 10]-NRT-code), using
  - OOA 4-folding and stacking with additional row [i] based on linear OA(27⁴¹, 8388601, F₂₇, 9) (dual of [8388601, 8388560, 10]-code), using
    - discarding factors / shortening the dual code based on linear OA(27⁴¹, large, F₂₇, 9) (dual of [large, large−41, 10]-code), using
      - the expurgated narrow-sense BCH-code C(I) with length 14348908Â | 27¹⁰âˆ’1, defining interval IÂ =Â [0,4], and minimum distance dÂ â‰¥ |{−4,−3,…,4}|+1Â =Â 10 (BCH-bound) [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.