MinT - Best Known (109−88, 109, s)-Nets in Base 9

Best Known (109−88, 109, s)-Nets in Base 9

(109−88, 109, 74)-Net over F₉ — Constructive and digital

Digital (21, 109, 74)-net over F₉, using

t-expansion [i] based on digital (17, 109, 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]

(109−88, 109, 88)-Net over F₉ — Digital

Digital (21, 109, 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]

(109−88, 109, 472)-Net in Base 9 — Upper bound on s

There is no (21, 109, 473)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 112 209363 742810 843010 425583 657805 729789 327007 674799 791922 672490 162351 125579 813417 277506 046864 183398 269153 > 9¹⁰⁹ [i]