MinT - Best Known (133−40, 133, s)-Nets in Base 3

Best Known (133−40, 133, s)-Nets in Base 3

(133−40, 133, 192)-Net over F₃ — Constructive and digital

Digital (93, 133, 192)-net over F₃, using

3¹ times duplication [i] based on digital (92, 132, 192)-net over F₃, using
- trace code for nets [i] based on digital (4, 44, 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]

(133−40, 133, 312)-Net over F₃ — Digital

Digital (93, 133, 312)-net over F₃, using

Gilbertâ€“VarÅ¡amov bound [i]

(133−40, 133, 6162)-Net in Base 3 — Upper bound on s

There is no (93, 133, 6163)-net in base 3, because

the generalized Rao bound for nets shows that 3^mÂ â‰¥ 2868 941546 988026 977843 152071 535063 443098 136140 777746 449989 291449 > 3¹³³ [i]