MinT - Best Known (69−48, 69, s)-Nets in Base 9

Best Known (69−48, 69, s)-Nets in Base 9

(69−48, 69, 74)-Net over F₉ — Constructive and digital

Digital (21, 69, 74)-net over F₉, using

t-expansion [i] based on digital (17, 69, 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]

(69−48, 69, 88)-Net over F₉ — Digital

Digital (21, 69, 88)-net over F₉, using

net from sequence [i] based on digital (21, 87)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 21 and N(F) ≥ 88, using
  - a curve from the manYPoints database [i]

(69−48, 69, 664)-Net in Base 9 — Upper bound on s

There is no (21, 69, 665)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 712189 212332 276649 426368 499886 263982 455094 933812 548573 870966 651841 > 9⁶⁹ [i]