MinT - Best Known (45, 45+76, s)-Nets in Base 9

Best Known (45, 45+76, s)-Nets in Base 9

(45, 45+76, 81)-Net over F₉ — Constructive and digital

Digital (45, 121, 81)-net over F₉, using

t-expansion [i] based on digital (32, 121, 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]

(45, 45+76, 147)-Net over F₉ — Digital

Digital (45, 121, 147)-net over F₉, using

t-expansion [i] based on digital (43, 121, 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]

(45, 45+76, 2029)-Net in Base 9 — Upper bound on s

There is no (45, 121, 2030)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 29 584827 510463 346120 380120 728403 365083 068003 493835 629761 400983 711861 804679 168442 338463 393377 143631 619455 593482 859617 > 9¹²¹ [i]