MinT - Best Known (109−76, 109, s)-Nets in Base 9

Best Known (109−76, 109, s)-Nets in Base 9

(109−76, 109, 81)-Net over F₉ — Constructive and digital

Digital (33, 109, 81)-net over F₉, using

t-expansion [i] based on digital (32, 109, 81)-net over F₉, using
- net from sequence [i] based on digital (32, 80)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 32 and N(F) ≥ 81, using
    - F₄ from the tower of function fields by Bezerra and GarcÃa over F₉ [i]

(109−76, 109, 128)-Net over F₉ — Digital

Digital (33, 109, 128)-net over F₉, using

net from sequence [i] based on digital (33, 127)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 33 and N(F) ≥ 128, using
  - a curve from the manYPoints database [i]

(109−76, 109, 1002)-Net in Base 9 — Upper bound on s

There is no (33, 109, 1003)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 105 693895 702083 461855 581925 111550 973028 941143 371853 804307 358605 582597 691419 066883 156628 005338 397927 436945 > 9¹⁰⁹ [i]