MinT - Best Known (134−59, 134, s)-Nets in Base 3

Best Known (134−59, 134, s)-Nets in Base 3

(134−59, 134, 80)-Net over F₃ — Constructive and digital

Digital (75, 134, 80)-net over F₃, using

trace code for nets [i] based on digital (8, 67, 40)-net over F₉, using
- net from sequence [i] based on digital (8, 39)-sequence over F₉, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₉ with g(F) = 8 and N(F) ≥ 40, using
    - a function field by SÃ©mirat [i]

(134−59, 134, 102)-Net over F₃ — Digital

Digital (75, 134, 102)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(134−59, 134, 871)-Net in Base 3 — Upper bound on s

There is no (75, 134, 872)-net in base 3, because

1 times m-reduction [i] would yield (75, 133, 872)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2871 934079 650904 864748 800615 226951 721059 338390 723416 961835 298257 > 3¹³³ [i]