MinT - Best Known (133−49, 133, s)-Nets in Base 9

Best Known (133−49, 133, s)-Nets in Base 9

(133−49, 133, 740)-Net over F₉ — Constructive and digital

Digital (84, 133, 740)-net over F₉, using

3 times m-reduction [i] based on digital (84, 136, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 68, 370)-net over F₈₁, using
  - net from sequence [i] based on digital (16, 369)-sequence over F₈₁, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 16 and N(F) ≥ 370, using
      - a function field by GarcÃa and Quoos [i]

(133−49, 133, 1056)-Net over F₉ — Digital

Digital (84, 133, 1056)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−49, 133, 217058)-Net in Base 9 — Upper bound on s

There is no (84, 133, 217059)-net in base 9, because

1 times m-reduction [i] would yield (84, 132, 217059)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 912047 405452 471386 576083 031827 341437 149576 817810 274491 366655 536740 875318 691141 753159 384905 946442 188749 858331 696722 382023 776321 > 9¹³² [i]