MinT - Best Known (29−25, 29, s)-Nets in Base 49

Best Known (29−25, 29, s)-Nets in Base 49

(29−25, 29, 54)-Net over F₄₉ — Constructive and digital

Digital (4, 29, 54)-net over F₄₉, using

net from sequence [i] based on digital (4, 53)-sequence over F₄₉, using
- Niederreiter sequence [i]

(29−25, 29, 92)-Net over F₄₉ — Digital

Digital (4, 29, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 29, 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]

(29−25, 29, 962)-Net in Base 49 — Upper bound on s

There is no (4, 29, 963)-net in base 49, because

1 times m-reduction [i] would yield (4, 28, 963)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 213332 791120 071879 881428 137822 212171 748399 653569 > 49²⁸ [i]