MinT - Best Known (66−50, 66, s)-Nets in Base 9

Best Known (66−50, 66, s)-Nets in Base 9

(66−50, 66, 64)-Net over F₉ — Constructive and digital

Digital (16, 66, 64)-net over F₉, using

t-expansion [i] based on digital (13, 66, 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]

(66−50, 66, 74)-Net over F₉ — Digital

Digital (16, 66, 74)-net over F₉, using

net from sequence [i] based on digital (16, 73)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 16 and N(F) ≥ 74, using
  - a curve from the manYPoints database [i]

(66−50, 66, 405)-Net in Base 9 — Upper bound on s

There is no (16, 66, 406)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 983 466906 110537 041326 515346 093442 048129 051621 735376 305333 050417 > 9⁶⁶ [i]