MinT - Best Known (66−49, 66, s)-Nets in Base 9

Best Known (66−49, 66, s)-Nets in Base 9

(66−49, 66, 74)-Net over F₉ — Constructive and digital

Digital (17, 66, 74)-net over F₉, using

net from sequence [i] based on digital (17, 73)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
  - a function field by GarcÃa and Quoos [i]

(66−49, 66, 456)-Net in Base 9 — Upper bound on s

There is no (17, 66, 457)-net in base 9, because

1 times m-reduction [i] would yield (17, 65, 457)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 110 180566 907767 690262 607534 123804 278979 509865 896466 567329 449921 > 9⁶⁵ [i]