MinT - Best Known (44−31, 44, s)-Nets in Base 9

Best Known (44−31, 44, s)-Nets in Base 9

(44−31, 44, 64)-Net over F₉ — Constructive and digital

Digital (13, 44, 64)-net over F₉, using

net from sequence [i] based on digital (13, 63)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 13 and N(F) ≥ 64, using
  - a function field by GarcÃa and Quoos [i]

(44−31, 44, 427)-Net in Base 9 — Upper bound on s

There is no (13, 44, 428)-net in base 9, because

1 times m-reduction [i] would yield (13, 43, 428)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 108240 935616 865239 008299 002606 050385 048609 > 9⁴³ [i]