MinT - Best Known (95−46, 95, s)-Nets in Base 9

Best Known (95−46, 95, s)-Nets in Base 9

(95−46, 95, 200)-Net over F₉ — Constructive and digital

Digital (49, 95, 200)-net over F₉, using

1 times m-reduction [i] based on 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]

(95−46, 95, 217)-Net over F₉ — Digital

Digital (49, 95, 217)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(95−46, 95, 10285)-Net in Base 9 — Upper bound on s

There is no (49, 95, 10286)-net in base 9, because

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]