MinT - Best Known (80−59, 80, s)-Nets in Base 9

Best Known (80−59, 80, s)-Nets in Base 9

(80−59, 80, 74)-Net over F₉ — Constructive and digital

Digital (21, 80, 74)-net over F₉, using

t-expansion [i] based on digital (17, 80, 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]

(80−59, 80, 88)-Net over F₉ — Digital

Digital (21, 80, 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]

(80−59, 80, 562)-Net in Base 9 — Upper bound on s

There is no (21, 80, 563)-net in base 9, because

1 times m-reduction [i] would yield (21, 79, 563)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 2469 706868 654583 774255 640408 871749 671853 867388 011529 501578 022522 554212 066105 > 9⁷⁹ [i]