MinT - Information on Result #1836698

Information on Result #1836698

OOA(9¹³⁸, 5593158, S₉, 3, 15), using (u,Â u+v)-construction based on

OOA(9²⁴, 756, S₉, 3, 7), using
- extracting embedded OOA [i] based on (17, 24, 756)-net in base 9, using
  - base change [i] based on digital (9, 16, 756)-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, 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]
      22. digital (0, 1, 28)-net over F₂₇ (see above)
      23. digital (0, 1, 28)-net over F₂₇ (see above)
      24. digital (0, 1, 28)-net over F₂₇ (see above)
      25. digital (0, 2, 28)-net over F₂₇, using
        kÂ =Â 2 construction [i]
      26. digital (0, 3, 28)-net over F₂₇, using
        net from sequence [i] based on digital (0, 27)-sequence over F₂₇, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 0 and N(F) ≥ 28, using
        the rational function field F₂₇(x) [i]
        Niederreiter sequence [i]
      27. digital (0, 7, 28)-net over F₂₇, using
        net from sequence [i] based on digital (0, 27)-sequence over F₂₇ (see above)
linear OOA(9¹¹⁴, 5592402, F₉, 3, 15) (dual of [(5592402, 3), 16777092, 16]-NRT-code), using
- trace code [i] based on linear OOA(81⁵⁷, 2796201, F₈₁, 3, 15) (dual of [(2796201, 3), 8388546, 16]-NRT-code), using
  - OOA 3-folding [i] based on linear OA(81⁵⁷, large, F₈₁, 15) (dual of [large, large−57, 16]-code), using
    - the expurgated narrow-sense BCH-code C(I) with length 21523361Â | 81⁸âˆ’1, defining interval IÂ =Â [0,7], and minimum distance dÂ â‰¥ |{−7,−6,…,7}|+1Â =Â 16 (BCH-bound) [i]

Mode: Constructive.

Optimality

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

Other Results with Identical Parameters

None.

Depending Results

None.