MinT - Best Known (36−25, 36, s)-Nets in Base 49

Best Known (36−25, 36, s)-Nets in Base 49

(36−25, 36, 61)-Net over F₄₉ — Constructive and digital

Digital (11, 36, 61)-net over F₄₉, using

net from sequence [i] based on digital (11, 60)-sequence over F₄₉, using
- Niederreiter sequence [i]

(36−25, 36, 92)-Net over F₄₉ — Digital

Digital (11, 36, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 36, 92)-net over F₄₉, using
- net from sequence [i] based on digital (3, 91)-sequence over F₄₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₄₉ with g(F) = 3 and N(F) ≥ 92, using
    - a curve from the manYPoints database [i]

(36−25, 36, 9366)-Net in Base 49 — Upper bound on s

There is no (11, 36, 9367)-net in base 49, because

1 times m-reduction [i] would yield (11, 35, 9367)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 143536 332802 375578 378639 781104 078479 440918 922036 013075 217345 > 49³⁵ [i]