MinT - Best Known (133−73, 133, s)-Nets in Base 9

Best Known (133−73, 133, s)-Nets in Base 9

(133−73, 133, 110)-Net over F₉ — Constructive and digital

Digital (60, 133, 110)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (7, 43, 36)-net over F₉, using
  - net from sequence [i] based on digital (7, 35)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 7 and N(F) ≥ 36, using
      - a function field by SÃ©mirat [i]
2. digital (17, 90, 74)-net over F₉, using
  - net from sequence [i] based on digital (17, 73)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 17 and N(F) ≥ 74, using
      - a function field by GarcÃa and Quoos [i]

(133−73, 133, 190)-Net over F₉ — Digital

Digital (60, 133, 190)-net over F₉, using

net from sequence [i] based on digital (60, 189)-sequence over F₉, using
- Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 60 and N(F) ≥ 190, using
  - Drinfeld modules of rank 1 [i]

(133−73, 133, 5608)-Net in Base 9 — Upper bound on s

There is no (60, 133, 5609)-net in base 9, because

1 times m-reduction [i] would yield (60, 132, 5609)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 915615 606642 177428 044148 879384 337542 717051 263937 562675 487084 733925 552359 675805 292792 418754 598071 876824 610898 548893 773690 119585 > 9¹³² [i]