MinT - Best Known (116−95, 116, s)-Nets in Base 9

Best Known (116−95, 116, s)-Nets in Base 9

(116−95, 116, 74)-Net over F₉ — Constructive and digital

Digital (21, 116, 74)-net over F₉, using

t-expansion [i] based on digital (17, 116, 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]

(116−95, 116, 88)-Net over F₉ — Digital

Digital (21, 116, 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]

(116−95, 116, 468)-Net in Base 9 — Upper bound on s

There is no (21, 116, 469)-net in base 9, because

1 times m-reduction [i] would yield (21, 115, 469)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 59 916101 372384 907588 456635 727801 020527 664148 543532 700636 209703 882388 370868 597595 963418 735833 970405 484468 915865 > 9¹¹⁵ [i]