MinT - Best Known (58, 135, s)-Nets in Base 9

Best Known (58, 135, s)-Nets in Base 9

(58, 135, 102)-Net over F₉ — Constructive and digital

Digital (58, 135, 102)-net over F₉, using

(u,Â u+v)-construction [i] based on
1. digital (3, 41, 28)-net over F₉, using
  - net from sequence [i] based on digital (3, 27)-sequence over F₉, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 3 and N(F) ≥ 28, using
      - the Hermitian function field over F₉ [i]
2. digital (17, 94, 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]

(58, 135, 182)-Net over F₉ — Digital

Digital (58, 135, 182)-net over F₉, using

t-expansion [i] based on digital (50, 135, 182)-net over F₉, using
- net from sequence [i] based on digital (50, 181)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 50 and N(F) ≥ 182, using
    - a curve from the manYPoints database [i]

(58, 135, 4328)-Net in Base 9 — Upper bound on s

There is no (58, 135, 4329)-net in base 9, because

1 times m-reduction [i] would yield (58, 134, 4329)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 74 111653 967213 236723 254068 506901 973230 754129 054522 119699 500401 483838 007585 050762 561397 058437 622201 470536 574653 931086 899725 172081 > 9¹³⁴ [i]