MinT - Best Known (68−47, 68, s)-Nets in Base 9

Best Known (68−47, 68, s)-Nets in Base 9

(68−47, 68, 74)-Net over F₉ — Constructive and digital

Digital (21, 68, 74)-net over F₉, using

t-expansion [i] based on digital (17, 68, 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]

(68−47, 68, 88)-Net over F₉ — Digital

Digital (21, 68, 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]

(68−47, 68, 695)-Net in Base 9 — Upper bound on s

There is no (21, 68, 696)-net in base 9, because

1 times m-reduction [i] would yield (21, 67, 696)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8602 518043 972710 428674 309664 539567 661569 516106 581663 278166 353729 > 9⁶⁷ [i]