MinT - Best Known (43, 43+76, s)-Nets in Base 9

Best Known (43, 43+76, s)-Nets in Base 9

(43, 43+76, 81)-Net over F₉ — Constructive and digital

Digital (43, 119, 81)-net over F₉, using

t-expansion [i] based on digital (32, 119, 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]

(43, 43+76, 147)-Net over F₉ — Digital

Digital (43, 119, 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]

(43, 43+76, 1804)-Net in Base 9 — Upper bound on s

There is no (43, 119, 1805)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 359310 653300 205038 868778 343726 185507 597356 129973 382070 790106 570581 852978 652874 616203 683878 028526 740550 704406 909105 > 9¹¹⁹ [i]