MinT - Best Known (4, 4+50, s)-Nets in Base 49

Best Known (4, 4+50, s)-Nets in Base 49

(4, 4+50, 54)-Net over F₄₉ — Constructive and digital

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

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

(4, 4+50, 92)-Net over F₄₉ — Digital

Digital (4, 54, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 54, 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]

(4, 4+50, 888)-Net in Base 49 — Upper bound on s

There is no (4, 54, 889)-net in base 49, because

14 times m-reduction [i] would yield (4, 40, 889)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 41 088966 398763 740281 328466 068448 579671 833172 781869 603508 312578 911585 > 49⁴⁰ [i]