MinT - Best Known (9, 34, s)-Nets in Base 49

Best Known (9, 34, s)-Nets in Base 49

(9, 34, 59)-Net over F₄₉ — Constructive and digital

Digital (9, 34, 59)-net over F₄₉, using

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

(9, 34, 92)-Net over F₄₉ — Digital

Digital (9, 34, 92)-net over F₄₉, using

t-expansion [i] based on digital (3, 34, 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, 34, 4893)-Net in Base 49 — Upper bound on s

There is no (9, 34, 4894)-net in base 49, because

1 times m-reduction [i] would yield (9, 33, 4894)-net in base 49, but
- the generalized Rao bound for nets shows that 49^mÂ â‰¥ 59 792036 481607 723608 537180 726228 055373 380510 640563 615105 > 49³³ [i]