MinT - Best Known (148, 148+67, s)-Nets in Base 3

Best Known (148, 148+67, s)-Nets in Base 3

(148, 148+67, 192)-Net over F₃ — Constructive and digital

Digital (148, 215, 192)-net over F₃, using

1 times m-reduction [i] based on digital (148, 216, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 72, 64)-net over F₂₇, using
  - net from sequence [i] based on digital (4, 63)-sequence over F₂₇, using
    - Niederreiterâ€“Xing sequence constructionÂ II/III [i] based on function field F/F₂₇ with g(F) = 4 and N(F) ≥ 64, using
      - a function field by SÃ©mirat [i]

(148, 148+67, 419)-Net over F₃ — Digital

Digital (148, 215, 419)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 148+67, 8140)-Net in Base 3 — Upper bound on s

There is no (148, 215, 8141)-net in base 3, because

1 times m-reduction [i] would yield (148, 214, 8141)-net in base 3, but
- the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1 272553 104287 315306 218683 847580 620505 950377 138949 302399 970262 957566 588276 372892 534269 277859 502721 294619 > 3²¹⁴ [i]