MinT - Best Known (9, 9+39, s)-Nets in Base 49

Best Known (9, 9+39, s)-Nets in Base 49

(9, 9+39, 59)-Net over F₄₉ — Constructive and digital

Digital (9, 48, 59)-net over F₄₉, using

net from sequence [i] based on digital (9, 58)-sequence over F₄₉, using
- Niederreiter sequence [i]

(9, 9+39, 92)-Net over F₄₉ — Digital

Digital (9, 48, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 48, 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]

(9, 9+39, 2496)-Net in Base 49 — Upper bound on s

There is no (9, 48, 2497)-net in base 49, because

1 times m-reduction [i] would yield (9, 47, 2497)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 27 568171 272884 568742 466326 169533 902760 971313 657957 134256 712583 658890 690032 423569 > 49⁴⁷ [i]