MinT - Best Known (148, 214, s)-Nets in Base 3

Best Known (148, 214, s)-Nets in Base 3

(148, 214, 204)-Net over F₃ — Constructive and digital

Digital (148, 214, 204)-net over F₃, using

3¹ times duplication [i] based on digital (147, 213, 204)-net over F₃, using
- trace code for nets [i] based on digital (5, 71, 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]

(148, 214, 431)-Net over F₃ — Digital

Digital (148, 214, 431)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(148, 214, 8140)-Net in Base 3 — Upper bound on s

There is no (148, 214, 8141)-net in base 3, because

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]