MinT - Best Known (81−65, 81, s)-Nets in Base 9

Best Known (81−65, 81, s)-Nets in Base 9

(81−65, 81, 64)-Net over F₉ — Constructive and digital

Digital (16, 81, 64)-net over F₉, using

t-expansion [i] based on digital (13, 81, 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]

(81−65, 81, 74)-Net over F₉ — Digital

Digital (16, 81, 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]

(81−65, 81, 369)-Net in Base 9 — Upper bound on s

There is no (16, 81, 370)-net in base 9, because

1 times m-reduction [i] would yield (16, 80, 370)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 23165 307088 851835 476144 417679 817816 753316 331877 385246 695938 161673 218548 106753 > 9⁸⁰ [i]