MinT - Best Known (11, 16, s)-Nets in Base 49

Best Known (11, 16, s)-Nets in Base 49

(11, 16, 120050)-Net over F₄₉ — Constructive and digital

Digital (11, 16, 120050)-net over F₄₉, using

generalized (u,Â u+v)-construction [i] based on
1. digital (0, 0, 2450)-net over F₄₉, using
  - s-reduction based on digital (0, 0, s)-net over F₄₉ with arbitrarily large s, using
    - arbitrary set of 49⁰ points [i]
2. digital (0, 0, 2450)-net over F₄₉ (see above)
3. digital (0, 0, 2450)-net over F₄₉ (see above)
4. digital (0, 0, 2450)-net over F₄₉ (see above)
5. digital (0, 0, 2450)-net over F₄₉ (see above)
6. digital (0, 0, 2450)-net over F₄₉ (see above)
7. digital (0, 0, 2450)-net over F₄₉ (see above)
8. digital (0, 0, 2450)-net over F₄₉ (see above)
9. digital (0, 0, 2450)-net over F₄₉ (see above)
10. digital (0, 0, 2450)-net over F₄₉ (see above)
11. digital (0, 0, 2450)-net over F₄₉ (see above)
12. digital (0, 0, 2450)-net over F₄₉ (see above)
13. digital (0, 0, 2450)-net over F₄₉ (see above)
14. digital (0, 0, 2450)-net over F₄₉ (see above)
15. digital (0, 0, 2450)-net over F₄₉ (see above)
16. digital (0, 0, 2450)-net over F₄₉ (see above)
17. digital (0, 0, 2450)-net over F₄₉ (see above)
18. digital (0, 0, 2450)-net over F₄₉ (see above)
19. digital (0, 0, 2450)-net over F₄₉ (see above)
20. digital (0, 0, 2450)-net over F₄₉ (see above)
21. digital (0, 0, 2450)-net over F₄₉ (see above)
22. digital (0, 0, 2450)-net over F₄₉ (see above)
23. digital (0, 0, 2450)-net over F₄₉ (see above)
24. digital (0, 0, 2450)-net over F₄₉ (see above)
25. digital (0, 0, 2450)-net over F₄₉ (see above)
26. digital (0, 0, 2450)-net over F₄₉ (see above)
27. digital (0, 0, 2450)-net over F₄₉ (see above)
28. digital (0, 0, 2450)-net over F₄₉ (see above)
29. digital (0, 0, 2450)-net over F₄₉ (see above)
30. digital (0, 0, 2450)-net over F₄₉ (see above)
31. digital (0, 0, 2450)-net over F₄₉ (see above)
32. digital (0, 0, 2450)-net over F₄₉ (see above)
33. digital (0, 0, 2450)-net over F₄₉ (see above)
34. digital (0, 0, 2450)-net over F₄₉ (see above)
35. digital (0, 0, 2450)-net over F₄₉ (see above)
36. digital (0, 0, 2450)-net over F₄₉ (see above)
37. digital (0, 0, 2450)-net over F₄₉ (see above)
38. digital (0, 0, 2450)-net over F₄₉ (see above)
39. digital (0, 0, 2450)-net over F₄₉ (see above)
40. digital (0, 0, 2450)-net over F₄₉ (see above)
41. digital (0, 0, 2450)-net over F₄₉ (see above)
42. digital (0, 0, 2450)-net over F₄₉ (see above)
43. digital (0, 0, 2450)-net over F₄₉ (see above)
44. digital (0, 0, 2450)-net over F₄₉ (see above)
45. digital (0, 1, 2450)-net over F₄₉, using
  - s-reduction based on digital (0, 1, s)-net over F₄₉ with arbitrarily large s, using
    - construction for strength kÂ =Â 1 [i]
46. digital (0, 1, 2450)-net over F₄₉ (see above)
47. digital (0, 1, 2450)-net over F₄₉ (see above)
48. digital (1, 3, 2450)-net over F₄₉, using
  - s-reduction based on digital (1, 3, 2451)-net over F₄₉, using
    - kÂ =Â 2 construction [i]
49. digital (5, 10, 2450)-net over F₄₉, using
  - generalized (u,Â u+v)-construction [i] based on
    1. digital (0, 0, 50)-net over F₄₉, using
      - s-reduction based on digital (0, 0, s)-net over F₄₉ with arbitrarily large s (see above)
    2. digital (0, 0, 50)-net over F₄₉ (see above)
    3. digital (0, 0, 50)-net over F₄₉ (see above)
    4. digital (0, 0, 50)-net over F₄₉ (see above)
    5. digital (0, 0, 50)-net over F₄₉ (see above)
    6. digital (0, 0, 50)-net over F₄₉ (see above)
    7. digital (0, 0, 50)-net over F₄₉ (see above)
    8. digital (0, 0, 50)-net over F₄₉ (see above)
    9. digital (0, 0, 50)-net over F₄₉ (see above)
    10. digital (0, 0, 50)-net over F₄₉ (see above)
    11. digital (0, 0, 50)-net over F₄₉ (see above)
    12. digital (0, 0, 50)-net over F₄₉ (see above)
    13. digital (0, 0, 50)-net over F₄₉ (see above)
    14. digital (0, 0, 50)-net over F₄₉ (see above)
    15. digital (0, 0, 50)-net over F₄₉ (see above)
    16. digital (0, 0, 50)-net over F₄₉ (see above)
    17. digital (0, 0, 50)-net over F₄₉ (see above)
    18. digital (0, 0, 50)-net over F₄₉ (see above)
    19. digital (0, 0, 50)-net over F₄₉ (see above)
    20. digital (0, 0, 50)-net over F₄₉ (see above)
    21. digital (0, 0, 50)-net over F₄₉ (see above)
    22. digital (0, 0, 50)-net over F₄₉ (see above)
    23. digital (0, 0, 50)-net over F₄₉ (see above)
    24. digital (0, 0, 50)-net over F₄₉ (see above)
    25. digital (0, 0, 50)-net over F₄₉ (see above)
    26. digital (0, 0, 50)-net over F₄₉ (see above)
    27. digital (0, 0, 50)-net over F₄₉ (see above)
    28. digital (0, 0, 50)-net over F₄₉ (see above)
    29. digital (0, 0, 50)-net over F₄₉ (see above)
    30. digital (0, 0, 50)-net over F₄₉ (see above)
    31. digital (0, 0, 50)-net over F₄₉ (see above)
    32. digital (0, 0, 50)-net over F₄₉ (see above)
    33. digital (0, 0, 50)-net over F₄₉ (see above)
    34. digital (0, 0, 50)-net over F₄₉ (see above)
    35. digital (0, 0, 50)-net over F₄₉ (see above)
    36. digital (0, 0, 50)-net over F₄₉ (see above)
    37. digital (0, 0, 50)-net over F₄₉ (see above)
    38. digital (0, 0, 50)-net over F₄₉ (see above)
    39. digital (0, 0, 50)-net over F₄₉ (see above)
    40. digital (0, 0, 50)-net over F₄₉ (see above)
    41. digital (0, 0, 50)-net over F₄₉ (see above)
    42. digital (0, 0, 50)-net over F₄₉ (see above)
    43. digital (0, 0, 50)-net over F₄₉ (see above)
    44. digital (0, 0, 50)-net over F₄₉ (see above)
    45. digital (0, 1, 50)-net over F₄₉, using
      - s-reduction based on digital (0, 1, s)-net over F₄₉ with arbitrarily large s (see above)
    46. digital (0, 1, 50)-net over F₄₉ (see above)
    47. digital (0, 1, 50)-net over F₄₉ (see above)
    48. digital (0, 2, 50)-net over F₄₉, using
      - kÂ =Â 2 construction [i]
    49. digital (0, 5, 50)-net over F₄₉, using
      - net from sequence [i] based on digital (0, 49)-sequence over F₄₉, using
        generalized Faure sequence [i]
        Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 0 and N(F) ≥ 50, using
        the rational function field F₄₉(x) [i]
        Niederreiter sequence [i]

(11, 16, 265827)-Net over F₄₉ — Digital

Digital (11, 16, 265827)-net over F₄₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(11, 16, large)-Net in Base 49 — Upper bound on s

There is no (11, 16, large)-net in base 49, because

3 times m-reduction [i] would yield (11, 13, large)-net in base 49, but
- mutually orthogonal hypercube bound [i]

Best Known (11, 16, s)-Nets in Base 49

(11, 16, 120050)-Net over F49 — Constructive and digital

(11, 16, 265827)-Net over F49 — Digital

(11, 16, large)-Net in Base 49 — Upper bound on s

(11, 16, 120050)-Net over F₄₉ — Constructive and digital

(11, 16, 265827)-Net over F₄₉ — Digital