MinT - Best Known (71, 140, s)-Nets in Base 9

Best Known (71, 140, s)-Nets in Base 9

(71, 140, 200)-Net over F₉ — Constructive and digital

Digital (71, 140, 200)-net over F₉, using

trace code for nets [i] based on digital (1, 70, 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]

(71, 140, 278)-Net over F₉ — Digital

Digital (71, 140, 278)-net over F₉, using

Gilbertâ€“VarÅ¡amov bound [i]

(71, 140, 13455)-Net in Base 9 — Upper bound on s

There is no (71, 140, 13456)-net in base 9, because

1 times m-reduction [i] would yield (71, 139, 13456)-net in base 9, but
- the generalized Rao bound for nets shows that 9^mÂ â‰¥ 4 373010 138825 410597 195620 603489 337653 543704 921460 490300 140005 338588 971446 197850 302094 480924 238543 905380 267975 291067 233104 643169 708801 > 9¹³⁹ [i]