MinT - Best Known (40, 40+76, s)-Nets in Base 9

Best Known (40, 40+76, s)-Nets in Base 9

(40, 40+76, 81)-Net over F₉ — Constructive and digital

Digital (40, 116, 81)-net over F₉, using

t-expansion [i] based on digital (32, 116, 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+76, 140)-Net over F₉ — Digital

Digital (40, 116, 140)-net over F₉, using

t-expansion [i] based on digital (39, 116, 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+76, 1513)-Net in Base 9 — Upper bound on s

There is no (40, 116, 1514)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 494 408987 191521 419433 164544 757699 745959 096484 506272 805412 538708 094687 936311 611579 746764 173848 172098 218493 971489 > 9¹¹⁶ [i]