MinT - Best Known (49, 49+47, s)-Nets in Base 9

Best Known (49, 49+47, s)-Nets in Base 9

(49, 49+47, 200)-Net over F₉ — Constructive and digital

Digital (49, 96, 200)-net over F₉, using

trace code for nets [i] based on digital (1, 48, 100)-net over F₈₁, using
- net from sequence [i] based on digital (1, 99)-sequence over F₈₁, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₈₁ with g(F) = 1 and N(F) ≥ 100, using
    - a function field by SÃ©mirat [i]

(49, 49+47, 209)-Net over F₉ — Digital

Digital (49, 96, 209)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(49, 49+47, 10285)-Net in Base 9 — Upper bound on s

There is no (49, 96, 10286)-net in base 9, because

1 times m-reduction [i] would yield (49, 95, 10286)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 505103 764462 050627 778162 387164 061307 585474 931405 157585 691263 203848 225297 694809 286316 594769 > 9⁹⁵ [i]