MinT - Best Known (21, 21+57, s)-Nets in Base 9

Best Known (21, 21+57, s)-Nets in Base 9

(21, 21+57, 74)-Net over F₉ — Constructive and digital

Digital (21, 78, 74)-net over F₉, using

t-expansion [i] based on digital (17, 78, 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]

(21, 21+57, 88)-Net over F₉ — Digital

Digital (21, 78, 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]

(21, 21+57, 577)-Net in Base 9 — Upper bound on s

There is no (21, 78, 578)-net in base 9, because

1 times m-reduction [i] would yield (21, 77, 578)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 30 615318 947828 578385 124528 491736 625793 923840 272929 198966 992344 789433 611585 > 9⁷⁷ [i]