MinT - Best Known (65, 65+33, s)-Nets in Base 9

Best Known (65, 65+33, s)-Nets in Base 9

(65, 65+33, 740)-Net over F₉ — Constructive and digital

Digital (65, 98, 740)-net over F₉, using

trace code for nets [i] based on digital (16, 49, 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]

(65, 65+33, 1353)-Net over F₉ — Digital

Digital (65, 98, 1353)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(65, 65+33, 518246)-Net in Base 9 — Upper bound on s

There is no (65, 98, 518247)-net in base 9, because

1 times m-reduction [i] would yield (65, 97, 518247)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 364 364721 654331 518624 607055 882457 991111 678967 014179 820126 331662 798577 499311 490118 289624 587137 > 9⁹⁷ [i]