MinT - Best Known (133−45, 133, s)-Nets in Base 9

Best Known (133−45, 133, s)-Nets in Base 9

(133−45, 133, 740)-Net over F₉ — Constructive and digital

Digital (88, 133, 740)-net over F₉, using

11 times m-reduction [i] based on digital (88, 144, 740)-net over F₉, using
- trace code for nets [i] based on digital (16, 72, 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]

(133−45, 133, 1675)-Net over F₉ — Digital

Digital (88, 133, 1675)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−45, 133, 601462)-Net in Base 9 — Upper bound on s

There is no (88, 133, 601463)-net in base 9, because

1 times m-reduction [i] would yield (88, 132, 601463)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 912052 324292 682307 788814 339071 629939 766175 407142 941586 125244 836313 592404 438277 349124 559170 108384 140426 281168 333499 166549 971153 > 9¹³² [i]