MinT - Best Known (40, 40+68, s)-Nets in Base 9

Best Known (40, 40+68, s)-Nets in Base 9

(40, 40+68, 81)-Net over F₉ — Constructive and digital

Digital (40, 108, 81)-net over F₉, using

t-expansion [i] based on digital (32, 108, 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]

(40, 40+68, 140)-Net over F₉ — Digital

Digital (40, 108, 140)-net over F₉, using

t-expansion [i] based on digital (39, 108, 140)-net over F₉, using
- net from sequence [i] based on digital (39, 139)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 39 and N(F) ≥ 140, using
    - a curve from the manYPoints database [i]

(40, 40+68, 1796)-Net in Base 9 — Upper bound on s

There is no (40, 108, 1797)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 11 441713 839827 498438 332278 654534 478622 160737 752772 674626 608400 237893 375006 606778 516296 709742 910641 966353 > 9¹⁰⁸ [i]