MinT - Best Known (10, 10+33, s)-Nets in Base 49

Best Known (10, 10+33, s)-Nets in Base 49

(10, 10+33, 60)-Net over F₄₉ — Constructive and digital

Digital (10, 43, 60)-net over F₄₉, using

net from sequence [i] based on digital (10, 59)-sequence over F₄₉, using
- Niederreiter sequence [i]

(10, 10+33, 92)-Net over F₄₉ — Digital

Digital (10, 43, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 43, 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]

(10, 10+33, 3865)-Net in Base 49 — Upper bound on s

There is no (10, 43, 3866)-net in base 49, because

1 times m-reduction [i] would yield (10, 42, 3866)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 97608 808936 085213 535977 817772 407095 404864 735264 839600 309046 874897 782273 > 49⁴² [i]