MinT - Best Known (45, 45+88, s)-Nets in Base 9

Best Known (45, 45+88, s)-Nets in Base 9

(45, 45+88, 81)-Net over F₉ — Constructive and digital

Digital (45, 133, 81)-net over F₉, using

t-expansion [i] based on digital (32, 133, 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+88, 147)-Net over F₉ — Digital

Digital (45, 133, 147)-net over F₉, using

t-expansion [i] based on digital (43, 133, 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+88, 1626)-Net in Base 9 — Upper bound on s

There is no (45, 133, 1627)-net in base 9, because

the generalized Rao bound for nets shows that 9^mÂ â‰¥ 8 422469 400209 623231 367019 683884 012150 501963 870058 379932 268146 580363 754512 594670 199694 682865 862923 196750 753732 680999 423148 089889 > 9¹³³ [i]