MinT - Best Known (5, 5+15, s)-Nets in Base 49

Best Known (5, 5+15, s)-Nets in Base 49

(5, 5+15, 55)-Net over F₄₉ — Constructive and digital

Digital (5, 20, 55)-net over F₄₉, using

net from sequence [i] based on digital (5, 54)-sequence over F₄₉, using
- Niederreiter sequence [i]

(5, 5+15, 92)-Net over F₄₉ — Digital

Digital (5, 20, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 20, 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]

(5, 5+15, 2721)-Net in Base 49 — Upper bound on s

There is no (5, 20, 2722)-net in base 49, because

1 times m-reduction [i] would yield (5, 19, 2722)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 130 012575 058686 974473 094800 849825 > 49¹⁹ [i]