MinT - Best Known (109−66, 109, s)-Nets in Base 9

Best Known (109−66, 109, s)-Nets in Base 9

(109−66, 109, 81)-Net over F₉ — Constructive and digital

Digital (43, 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]

(109−66, 109, 147)-Net over F₉ — Digital

Digital (43, 109, 147)-net over F₉, using

net from sequence [i] based on digital (43, 146)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 43 and N(F) ≥ 147, using
  - a curve from the manYPoints database [i]

(109−66, 109, 2314)-Net in Base 9 — Upper bound on s

There is no (43, 109, 2315)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 104 041126 449416 764248 147144 979309 672688 040960 065313 353038 556147 274722 933904 628162 814672 025379 906709 199705 > 9¹⁰⁹ [i]