MinT - Information on Result #1230858

Information on Result #1230858

Digital (84, 96, 2797502)-net over F₂₅, using generalized (u,Â u+v)-construction based on

digital (0, 2, 26)-net over F₂₅, using
- kÂ =Â 2 construction [i]
digital (1, 4, 626)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25⁴, 626, F₂₅, 3, 3) (dual of [(626, 3), 1874, 4]-NRT-code), using
  - appending kth column [i] based on linear OOA(25⁴, 626, F₂₅, 2, 3) (dual of [(626, 2), 1248, 4]-NRT-code), using
    - OAs with strength 3, bÂ â‰ Â 2, and mÂ >Â 3 are always embeddable [i] based on linear OA(25⁴, 626, F₂₅, 3) (dual of [626, 622, 4]-code or 626-cap in PG(3,25)), using
      - ovoid in PG(3,Â 25) [i]
digital (4, 8, 650)-net over F₂₅, using
- generalized (u,Â u+v)-construction [i] based on
  1. digital (0, 0, 26)-net over F₂₅, using
    - s-reduction based on digital (0, 0, s)-net over F₂₅ for arbitrarily large s, using
      - arbitrary set of 25⁰ points [i]
  2. digital (0, 0, 26)-net over F₂₅ (see above)
  3. digital (0, 0, 26)-net over F₂₅ (see above)
  4. digital (0, 0, 26)-net over F₂₅ (see above)
  5. digital (0, 0, 26)-net over F₂₅ (see above)
  6. digital (0, 0, 26)-net over F₂₅ (see above)
  7. digital (0, 0, 26)-net over F₂₅ (see above)
  8. digital (0, 0, 26)-net over F₂₅ (see above)
  9. digital (0, 0, 26)-net over F₂₅ (see above)
  10. digital (0, 0, 26)-net over F₂₅ (see above)
  11. digital (0, 0, 26)-net over F₂₅ (see above)
  12. digital (0, 0, 26)-net over F₂₅ (see above)
  13. digital (0, 0, 26)-net over F₂₅ (see above)
  14. digital (0, 0, 26)-net over F₂₅ (see above)
  15. digital (0, 0, 26)-net over F₂₅ (see above)
  16. digital (0, 0, 26)-net over F₂₅ (see above)
  17. digital (0, 0, 26)-net over F₂₅ (see above)
  18. digital (0, 0, 26)-net over F₂₅ (see above)
  19. digital (0, 0, 26)-net over F₂₅ (see above)
  20. digital (0, 0, 26)-net over F₂₅ (see above)
  21. digital (0, 0, 26)-net over F₂₅ (see above)
  22. digital (0, 1, 26)-net over F₂₅, using
    - s-reduction based on digital (0, 1, s)-net over F₂₅ for arbitrarily large s, using
      - construction for strength kÂ =Â 1 [i]
  23. digital (0, 1, 26)-net over F₂₅ (see above)
  24. digital (0, 2, 26)-net over F₂₅ (see above)
  25. digital (0, 4, 26)-net over F₂₅, using
    - net from sequence [i] based on digital (0, 25)-sequence over F₂₅, using
      - generalized Faure sequence [i]
      - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₅ with g(F) = 0 and N(F) ≥ 26, using
        the rational function field F₂₅(x) [i]
      - Niederreiter sequence [i]
digital (20, 26, 1398100)-net over F₂₅, using
- s-reduction based on digital (20, 26, 2796201)-net over F₂₅, using
  - net defined by OOA [i] based on linear OOA(25²⁶, 2796201, F₂₅, 6, 6) (dual of [(2796201, 6), 16777180, 7]-NRT-code), using
    - OA 3-folding and stacking [i] based on linear OA(25²⁶, large, F₂₅, 6) (dual of [large, large−26, 7]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,5], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 7 [i]
digital (44, 56, 1398100)-net over F₂₅, using
- net defined by OOA [i] based on linear OOA(25⁵⁶, 1398100, F₂₅, 12, 12) (dual of [(1398100, 12), 16777144, 13]-NRT-code), using
  - OA 6-folding and stacking [i] based on linear OA(25⁵⁶, 8388600, F₂₅, 12) (dual of [8388600, 8388544, 13]-code), using
    - discarding factors / shortening the dual code based on linear OA(25⁵⁶, large, F₂₅, 12) (dual of [large, large−56, 13]-code), using
      - the primitive expurgated narrow-sense BCH-code C(I) with length 9765624Â = 25⁵âˆ’1, defining interval IÂ =Â [0,11], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [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.