MinT - Best Known (73, 73+29, s)-Nets in Base 3

Best Known (73, 73+29, s)-Nets in Base 3

(73, 73+29, 204)-Net over F₃ — Constructive and digital

Digital (73, 102, 204)-net over F₃, using

trace code for nets [i] based on digital (5, 34, 68)-net over F₂₇, using
- net from sequence [i] based on digital (5, 67)-sequence over F₂₇, using
  - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 5 and N(F) ≥ 68, using
    - a function field by SÃ©mirat [i]

(73, 73+29, 311)-Net over F₃ — Digital

Digital (73, 102, 311)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(73, 73+29, 8352)-Net in Base 3 — Upper bound on s

There is no (73, 102, 8353)-net in base 3, because

1 times m-reduction [i] would yield (73, 101, 8353)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 547456 231960 050247 116307 116134 483443 588222 077881 > 3¹⁰¹ [i]