MinT - Best Known (145−44, 145, s)-Nets in Base 3

Best Known (145−44, 145, s)-Nets in Base 3

(145−44, 145, 192)-Net over F₃ — Constructive and digital

Digital (101, 145, 192)-net over F₃, using

3¹ times duplication [i] based on digital (100, 144, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 48, 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]

(145−44, 145, 325)-Net over F₃ — Digital

Digital (101, 145, 325)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(145−44, 145, 6295)-Net in Base 3 — Upper bound on s

There is no (101, 145, 6296)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 1527 012594 185159 088400 458001 318044 638282 889006 304510 700388 267218 261649 > 3¹⁴⁵ [i]